]>
2016
9
12
ISSN 2008-1898
523
Some integral inequalities of the Hermite--Hadamard type for log-convex functions on co-ordinates
Some integral inequalities of the Hermite--Hadamard type for log-convex functions on co-ordinates
en
en
In the paper, the authors establish some new integral inequalities for log-convex functions on co-ordinates.
These newly-established inequalities are connected with integral inequalities of the Hermite-Hadamard type
for log-convex functions on co-ordinates.
5900
5908
Yu-Mei
Bai
College of Mathematics
Inner Mongolia University for Nationalities
China
baiym2008@sohu.com
Feng
Qi
Department of Mathematics, College of Science
Institute of Mathematics
Tianjin Polytechnic University
Henan Polytechnic University
China
China
qifeng618@gmail.com;qifeng618@hotmail.com
Log-convex functions
co-ordinates
integral inequality
Hermite-Hadamard type.
Article.1.pdf
[
[1]
M. Alomari, M. Darus, On the Hadamard's inequality for log-convex functions on the coordinates, J. Inequal. Appl., 2009 (2009), 1-13
##[2]
S.-P. Bai, F. Qi, S.-H. Wang, Some new integral inequalities of Hermite-Hadamard type for (\(\alpha,m,P\))-convex functions on co-ordinates, J. Appl. Anal. Comput., 6 (2016), 171-178
##[3]
S. S. Dragomir, On the Hadamards inequlality for convex functions on the co-ordinates in a rectangle from the plane, Taiwanese J. Math., 5 (2001), 775-788
##[4]
S. S. Dragomir, C. E. M. Pearce, Selected topics on Hermite-Hadamard inequalities and applications, RGMIA Monographs, Victoria University (2002)
##[5]
P. M. Gill, C. E. M. Pearce, J. Pečarić, Hadamard's inequality for r-convex functions, J. Math. Anal. Appl., 215 (1997), 461-470
##[6]
X.-Y. Guo, F. Qi, B.-Y. Xi, Some new inequalities of Hermite-Hadamard type for geometrically mean convex functions on the co-ordinates, J. Comput. Anal. Appl., 21 (2016), 144-155
##[7]
D.-Y. Hwang, K.-L. Tseng, G.-S. Yang, Some Hadamard's inequalities for co-ordinated convex functions in a rectangle from the plane, Taiwanese J. Math., 11 (2007), 63-73
##[8]
M. Klaričić Bakula, J. Pečarić, On the Jensen's inequality for convex functions on the co-ordinates in a rectangle from the plane, Taiwanese J. Math., 10 (2006), 1271-1292
##[9]
M. E. Özdemir, A. O. Akdemir, H. Kavurmacı, On the Simpsons inequality for co-ordinated convex functions, Turkish J. Anal. Number Theory, 2 (2014), 165-169
##[10]
M. E. Özdemir, A. O. Akdemir, Ç . Yıldız, On co-ordinated quasi-convex functions, Czechoslovak Math. J., 62 (2012), 889-900
##[11]
M. E. Özdemir, E. Set, M. Z. Sarikaya, Some new Hadamard type inequalities for co-ordinated m-convex and (\(\alpha,m\))-convex functions, Hacet. J. Math. Stat., 40 (2011), 219-229
##[12]
M. E. Özdemir, Ç . Yıldız, A. O. Akdemir, On some new Hadamard-type inequalities for co-ordinated quasi-convex functions, Hacet. J. Math. Stat., 41 (2012), 697-707
##[13]
F. Qi, B.-Y. Xi, Some integral inequalities of Simpson type for \(GA-\varepsilon\)-convex functions, Georgian Math. J., 20 (2013), 775-788
##[14]
M. Z. Sarikaya, On the Hermite-Hadamard-type inequalities for co-ordinated convex function via fractional integrals, Integral Transforms Spec. Funct., 25 (2014), 134-147
##[15]
M. Z. Sarikaya, Some inequalities for differentiable coordinated convex mappings, Asian-Eur. J. Math., 8 (2015), 1-21
##[16]
M. Z. Sarikaya, H. Budak, H. Yaldiz, Čebyševtype inequalities for co-ordinated convex functions, Pure Appl. Math. Lett., 2 (2014), 36-40
##[17]
M. Z. Sarikaya, H. Budak, H. Yaldiz, Some new Ostrowski type inequalities for co-ordinated convex functions, Turkish J. Anal. Number Theory, 2 (2014), 176-182
##[18]
M. Z. Sarikaya, E. Set, M. E. Ozdemir, S. S. Dragomir, New some Hadamard's type inequalities for co-ordinated convex functions, Tamsui Oxf. J. Inf. Math. Sci., 28 (2012), 137-152
##[19]
E. Set, M. Z. Sarikaya, A. O. Akdemir, Hadamard type inequalities for \(\varphi\)-convex functions on co-ordinates, Tbilisi Math. J., 7 (2014), 51-60
##[20]
E. Set, M. Z. Sarikaya, H. Ögülmüş, Some new inequalities of Hermite-Hadamard type for h-convex functions on the co-ordinates via fractional integrals, Facta Univ. Ser. Math. Inform., 29 (2014), 397-414
##[21]
S.-H. Wang, F. Qi, Hermite-Hadamard type inequalities for s-convex functions via Riemann-Liouville fractional integrals, J. Comput. Anal. Appl., 22 (2017), 1124-1134
##[22]
Y. Wang, B.-Y. Xi, F. Qi, Integral inequalities of Hermite-Hadamard type for functions whose derivatives are strongly \(\alpha\)-preinvex, Acta Math. Acad. Paedagog. Nyházi. (N.S.), 32 (2016), 79-87
##[23]
Y. Wu, F. Qi,, On some Hermite-Hadamard type inequalities for (s;QC)-convex functions, SpringerPlus, 5 (2016), 1-13
##[24]
B.-Y. Xi, F. Qi, Integral inequalities of Simpson type for logarithmically convex functions, Adv. Stud. Contemp. Math. (Kyungshang), 23 (2013), 559-566
##[25]
J. Zhang, F. Qi, G.-C. Xu, Z.-L. Pei, Hermite-Hadamard type inequalities for n-times differentiable and geometrically quasi-convex functions, SpringerPlus, 5 (2016), 1-6
]
Common fixed point theorems for six self-maps in \(b\)-metric spaces with nonlinear contractive conditions
Common fixed point theorems for six self-maps in \(b\)-metric spaces with nonlinear contractive conditions
en
en
In the framework of a b-metric space, by using the compatible and weak compatible conditions of self-
mapping pair, we discussed the existence and uniqueness of the common fixed point for a class of \(\phi\)-type
contraction mapping, some new common fixed point theorems are obtained. In the end of the paper, we
give some illustrative examples in support of our new results. The results presented in this paper extend
and improve some well-known comparable results in the existing literature.
5909
5930
Liya
Liu
Institute of Applied Mathematics and Department of Mathematics
Hangzhou Normal University
China
846883245@qq.com
Feng
Gu
Institute of Applied Mathematics and Department of Mathematics
Hangzhou Normal University
China
gufeng_99@sohu.com
\(b\)-metric space
common fixed point
compatible maps
weak compatible maps.
Article.2.pdf
[
[1]
A. Aghajani, M. Abbas, J. R. Roshan, Common fixed point of generalized weak contractive mappings in partially ordered b-metric spaces, Math. Slovaca, 64 (2014), 941-960
##[2]
M. A. Akkouchi, A common fixed point theorem for expansive mappings under strict implicit conditions on b- metric spaces, Acta Univ. Palack. Olomuc. Fac. Rerum Natur. Math., 50 (2011), 5-15
##[3]
M. Boriceanu, Strict fixed point theorems for multivalued operators in b-metric spaces, Int. J. Mod. Math., 4 (2009), 285-301
##[4]
M. Boriceanu, M. Bota, A. Petruşel, Multivalued fractals in b-metric spaces, Cent. Eur. J. Math., 8 (2010), 367-377
##[5]
S. S. Chang, S. K. Kang, N. J. Huang, Fixed point theorems for the pair of mappings in 2-metric space, J. Chengdu Univ. Sci. Technol., 2 (1984), 107-114
##[6]
S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostraviensis, 1 (1993), 5-11
##[7]
X. P. Ding, Some common fixed point theorems of commuting mappings, II, Math. Sem. Notes Kobe Univ., 11 (1983), 301-305
##[8]
M. L. Diviccaro, S. Sessa, Some remarks on common fixed points of four mappings, Jñānābha, 15 (1985), 139-149
##[9]
N. N. Fang, F. Gu, Two pairs of self-mappings common fixed point theorem in b-metric space, J. Hangzhou Normal Univ., Natur. Sci. Ed., 15 (2016), 282-289
##[10]
G. Jungck, Compatible mappings and common fixed points, II, Internat. J. Math. Math. Sci., 11 (1988), 285-288
##[11]
G. Jungck, Common fixed points for noncontinuous nonself maps on nonmetric space, Far East J. Math. Sci., 4 (1996), 199-212
##[12]
S. M. Kang, Y. J. Cho, G. Jungck, Common fixed points of compatible mappings, Internat. J. Math. Math. Sci., 13 (1990), 61-66
##[13]
H. Li, F. Gu, A new common fixed point theorem of four maps in b-metric spaces, J. Hangzhou Norm. Univ., Natur. Sci. Ed., 15 (2016), 75-80
##[14]
H. Li, F. Gu, A new common fixed point theorem of third power type contractive mappings in b-metric spaces, J. Hangzhou Norm. Univ., Natur. Sci. Ed., 15 (2016), 401-407
##[15]
L. L. Liu, The common fixed point theorem of (sub)compatible mappings and general ishikawa iterative loomed theorem, J. Qufu Normal Univ., Natur. Sci. Ed., 16 (1990), 40-44
##[16]
L. Liu, F. Gu, The common fixed point theorem for a class of twice power type \(\Phi\)-contractive mapping in b-metric spaces, J. Hangzhou Norm. Univ., Natur. Sci. Ed., 15 (2016), 171-177
##[17]
S. Phiangsungnoen, W. Sintunavarat, P. Kumam, Fixed point results, generalized Ulam-Hyers stability and well- posedness via \(\alpha\)-admissible mappings in b-metric spaces, Fixed Point Theory Appl., 2014 (2014), 1-17
##[18]
J. R. Roshan, N. Shobkolaei, S. Sedghi, M. Abbas, Common fixed point of four maps in b-metric spaces, Hacet. J. Math. Stat., 43 (2014), 613-624
##[19]
W. Shatanawi, A. Pitea, R. Lazovié, Contraction conditions using comparison functions on b-metric spaces, Fixed Point Theory Appl., 2014 (2014), 1-11
##[20]
J. Yu, F. Gu, A new common fixed point theorem of six mappings in metric space, J. Hangzhou Norm. Univ., Natur. Sci. Ed., 5 (2011), 393-398
]
Some new coupled fixed point theorems in ordered partial \(b\)-metric spaces
Some new coupled fixed point theorems in ordered partial \(b\)-metric spaces
en
en
In this paper, we establish some new coupled fixed point theorems in ordered partial \(b\)-metric spaces.
Also, an example is provided to support our new results. The results presented in this paper extend and
improve several well-known comparable results.
5931
5949
Hedong
Li
Institute of Applied Mathematics and Department of Mathematics
Hangzhou Normal University
China
375885597@qq.com
Feng
Gu
Institute of Applied Mathematics and Department of Mathematics
Hangzhou Normal University
China
gufeng_99@sohu.com
Common coupled fixed point
coupled coincidence point
partially ordered set
mixed \(g\)-monotone property
partial \(b\)-metric space.
Article.3.pdf
[
[1]
M. Abbas, M. Ali Khan, S. Radenović, Common coupled fixed point theorems in cone metric spaces for w- compatible mappings, Appl. Math. Comput., 217 (2010), 195-202
##[2]
T. Abdeljawad, Fixed points for generalized weakly contractive mappings in partial metric spaces, Math. Comput. Modelling, 54 (2011), 2923-2927
##[3]
T. Abdeljawad, E. Karapınar, K. Taş, Existence and uniqueness of a common fixed point on partial metric spaces, Appl. Math. Lett., 24 (2011), 1900-1904
##[4]
A. Aghajani, R. Arab, Fixed points of (\(\psi,\phi,\theta\))-contractive mappings in partially ordered b-metric spaces and application to quadratic integral equations, Fixed Point Theory Appl., 2013 (2013), 1-20
##[5]
M. Akkouchi, A common fixed point theorem for expansive mappings under strict implicit conditions on b-metric spaces, Acta Univ. Palack. Olomuc. Fac. Rerum Natur. Math., 50 (2011), 5-15
##[6]
H. Aydi, E. Karapınar, W. Shatanawi, Coupled fixed point results for \(\phi,\psi\) -weakly contractive condition in ordered partial metric spaces, Comput. Math. Appl., 62 (2011), 4449-4460
##[7]
S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostraviensis, 1 (1993), 5-11
##[8]
R. George, K. P. Reshma, A. Padmavati, Fixed point theorems for cyclic contractions in b-metric spaces, J. Nonlinear Funct. Anal., 2015 (2015), 1-22
##[9]
T. Gnana Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal., 65 (2006), 1379-1393
##[10]
A. Gupta, P. Gautam, Some coupled fixed point theorems on quasi-partial b-metric spaces, Int. J. Math. Anal., 9 (2015), 293-306
##[11]
J. Harjani, B. López, K. Sadarangani, Fixed point theorems for mixed monotone operators and applications to integral equations, Nonlinear Anal., 74 (2011), 1749-1760
##[12]
M. S. Khan, M. Swaleh, S. Sessa, Fixed point theorems by altering distances between the points, Bull. Austral. Math. Soc., 30 (1984), 1-9
##[13]
J. K. Kim, T. M. Tuyen, Approximation common zero of two accretive operators in Banach spaces, Appl. Math. Comput., 283 (2016), 265-281
##[14]
V. Lakshmikantham, L. Ćirić, Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Anal., 70 (2009), 4341-4349
##[15]
H. Li, F. Gu, A new common fixed point theorem for four maps in b-metric spaces, J. Hangzhou Norm. Univ., Nat. Sci. Ed., 15 (2016), 75-80
##[16]
L. Liu, F. Gu, The common fixed point theorem for a class of twice power type \(\Phi\)-contractive mapping in b-metric spaces, J. Hangzhou Norm. Univ., Nat. Sci. Ed., 15 (2016), 171-177
##[17]
N. V. Luong, N. X. Thuan, Coupled fixed points in partially ordered metric spaces and application, Nonlinear Anal., 74 (2011), 983-992
##[18]
Partial metric topology, Papers on general topology and applications, S. G. Matthews, Flushing, NY, (1992), 183-197, Ann. New York Acad. Sci., New York Acad. Sci., New York (1994)
##[19]
Z. Mustafa, J. R. Roshan, V. Parvaneh, Z. Kadelburg, Some common fixed point results in ordered partial b-metric spaces, J. Inequal. Appl., 2013 (2013), 1-26
##[20]
H. K. Nashine, W. Shatanawi, Coupled common fixed point theorems for a pair of commuting mappings in partially ordered complete metric spaces, Comput. Math. Appl., 62 (2011), 1984-1993
##[21]
X. L. Qin, J.-C. Yao, Weak convergence of a Mann-like algorithm for nonexpansive and accretive operators, J. Inequal. Appl., 2016 (2016), 1-9
##[22]
H. Piri, Some Suzuki type fixed point theorems in complete cone b-metric spaces over a solid vector space, Commun. Optim. Theory, 2016 (2016), 1-15
##[23]
K. P. R. Rao, K. V. Siva Parvathi, M. Imdad, A coupled coincidence point theorem on ordered partial b-metric-like spaces, Electron. J. Math. Anal. Appl., 3 (2015), 141-149
##[24]
J. R. Roshan, V. Parvaneh, I. Altun, Some coincidence point results in ordered b-metric spaces and applications in a system of integral equations, Appl. Math. Comput., 226 (2014), 725-737
##[25]
G. S. Saluja, Some fixed point theorems for generalized contractions involving rational expressions in b-metric spaces, Commun. Optim. Theory, 2016 (2016), 1-13
##[26]
S. Shukla, Partial b-metric spaces and fixed point theorems, Mediterr. J. Math., 11 (2013), 703-711
##[27]
J. Zhao, S. Wang, Viscosity approximation method for the split common fixed point problem of quasi-strict pseu- docontractions without prior knowledge of operator norms, Noninear Funct. Anal. Appl., 20 (2015), 199-213
]
Coupled coincidence point results for Geraghty-type contraction by using monotone property in partially ordered \(S\)-metric spaces
Coupled coincidence point results for Geraghty-type contraction by using monotone property in partially ordered \(S\)-metric spaces
en
en
In this paper, we introduce a new concept of generalized compatibility for a pair of mappings defined on
a product \(S\)-metric and prove certain coupled coincidence point results for mappings satisfying Geraghty-
type contraction by using g-monotone instead of the usually mixed monotone property. We also give
some sufficient conditions for the uniqueness of a coupled coincidence point. Our results generalize the
corresponding results of Zhou and Liu [M. Zhou, X.-L. Liu, J. Funct. Spaces, 2016 (2016), 9 pages],
without mixed weakly monotone property and Kadelburg et al. [Z. Kadelburg, P. Kuman, S. Radenović,
W. Sintunavarat, Fixed Point Theory Appl., 2015 (2015), 14 pages] from usually metric to \(S\)-metric. An
illustrative example is presented to support our results.
5950
5969
Mi
Zhou
School of Science and Technology
Sanya College
China
mizhou330@126.com
Xiao-lan
Liu
College of Science
Sichuan University of Science and Engineering
Sichuan Province University Key Laboratory of Bridge Non-destruction Detecting and Engineering Computing
China
China
stellalwp@163.com
Diana
Dolićanin-Dekić
Faculty of Technical Science
University of Pristina-Kosovska Mitrovica
Serbia
diana.dolicanin@pr.ac.rs
Boško
Damjanović
Faculty of Agriculture
University of Belgrade
Serbia
dambo@agrif.bg.ac.rs
Coupled coincidence point
generalized compatibility
monotone property
partially ordered \(S\)-metric space
Geraghty-type contraction.
Article.4.pdf
[
[1]
M. Borcut, Tripled coincidence theorems for monotone mappings in partially ordered metric spaces, Creat. Math. Inform., 21 (2012), 135-142
##[2]
M. Borcut, Tripled fixed point theorems for monotone mappings in partially ordered metric spaces, Carpathian J. Math., 28 (2012), 207-214
##[3]
N. V. Dung, On coupled common fixed points for mixed weakly monotone maps in partially ordered S-metric spaces, Fixed Point Theory Appl., 2013 (2013), 1-17
##[4]
T. Gnana Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal., 65 (2006), 1379-1393
##[5]
M. E. Gordji, E. Akbartabar, Y. J. Cho, M. Ramezani, Coupled common fixed point theorems for mixed weakly monotone mappings in partially ordered metric spaces, Fixed Point Theory Appl., 2012 (2012), 1-12
##[6]
Z. Kadelburg, P. Kuman, S. Radenović, W. Sintunavarat, Common coupled fixed point theorems for Geraghty-type contraction mappings using monotone property, Fixed Point Theory Appl., 2015 (2015), 1-14
##[7]
Z. Kadelburg, S. Radenović, Remarks on some recent M. Borcut's results in partially ordered metric spaces, Int. J. Nonlinear Anal. Appl., 6 (2015), 96-104
##[8]
V. Lakshmikantham, L. Ćirić, Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Anal., 70 (2009), 4341-4349
##[9]
S. Radenović, Bhaskar-Lakshmikantham type results for monotone mappings in partially ordered metric spaces, Int. J. Nonlinear Anal. Appl., 5 (2014), 96-103
##[10]
S. Radenović, Coupled fixed point theorems for monotone mappings in partially ordered metric spaces, Kragujevac J. Math., 38 (2014), 249-257
##[11]
S. Radenović, Some coupled coincidence points results of monotone mappings in partially ordered metric spaces, Int. J. Nonlinear Anal. Appl., 5 (2014), 174-184
##[12]
S. Sedghi, N. V. Dung, Fixed point theorems on S-metric spaces, Mat. Vensnik, 66 (2014), 113-124
##[13]
S. Sedghi, N. Shobe, A. Aliouche, A generalization of fixed point theorems in S-metric spaces, Mat. Vesnik, 64 (2012), 258-266
##[14]
M. Zhou, X.-L. Liu, Coupled common fixed point theorems for Geraghty-type contraction mappings using mixed weakly monotone property in partially ordered S-metric spaces, J. Funct. Spaces, 2016 (2016), 1-9
]
Hyers-Ulam stability of derivations in fuzzy Banach space
Hyers-Ulam stability of derivations in fuzzy Banach space
en
en
In this paper, we construct an additive functional equation, and use the fixed point alternative theorem to
investigate the Hyers-Ulam stability of derivations fuzzy Banach space and fuzzy Lie Banach space associated
with the following functional equation:\( f (2x - y - z)+f (x - z)+f (x + y + 2z) = f (4x)\).
5970
5979
Gang
Lu
Department of Mathematics
Department of Mathematics, School of Science
Zhejiang University
Shenyang University of Technology
P. R. China
P. R. China
lvgang1234@hanmail.net
Jun
Xie
Department of Mathematics, School of Science
Shenyang University of Technology
P. R. China
583193617@qq.com
Qi
Liu
Department of Mathematics, School of Science
Shenyang University of Technology
P. R. China
903037649@qq.com
Yuanfeng
Jin
Department of Mathematics
Yanbian University
P. R. China
yfkim@ybu.edu.cn
Fuzzy normed space
additive functional equation
Hyers-Ulam stability
fixed point alternative
fuzzy Banach space.
Article.5.pdf
[
[1]
S. Alizadeh, F. Moradlou, Approximate a quadratic mapping in multi-Banach spaces, a fixed point approach, Int. J. Nonlinear Anal. Appl., 7 (2016), 63-75
##[2]
T. Aoki, On the stability of the linear transformation in Banach spaces, J. Math. Soc. Japan, 2 (1950), 64-66
##[3]
T. Bag, S. K. Samanta, Finite dimensional fuzzy normed linear spaces, J. Fuzzy Math., 11 (2003), 687-705
##[4]
T. Bag, S. K. Samanta, Fuzzy bounded linear operators, Fuzzy Sets and Systems, 151 (2005), 513-547
##[5]
V. Balopoulos, A. G. Hatzimichailidis, B. K. Papadopoulos, Distance and similarity measures for fuzzy operators, Inform. Sci., 177 (2007), 2336-2348
##[6]
R. Biswas, Fuzzy inner product spaces and fuzzy norm functions, Inform. Sci., 53 (1991), 185-190
##[7]
N. Brillouët-Belluot, J. Brzdęk, K. Ciepliński, On some recent developments in Ulam's type stability,, Abstr. Appl. Anal., 2012 (2012), 1-41
##[8]
J. Brzdęk, Hyperstability of the Cauchy equation on restricted domains, Acta Math. Hungar., 141 (2013), 58-67
##[9]
J. Brzdęk, J. Chudziak, Z. Páles, A fixed point approach to stability of functional equations, Nonlinear Anal., 74 (2011), 6728-6732
##[10]
J. Brzdęk, K. Ciepliński, Hyperstability and superstability, Abstr. Appl. Anal., 2013 (2013), 1-13
##[11]
J. Brzdęk, A. Fošner, Remarks on the stability of Lie homomorphisms, J. Math. Anal. Appl., 400 (2013), 585-596
##[12]
L. Cădariu, L. Găvruţa, P. Găvruţa, Fixed points and generalized Hyers-Ulam stability, Abstr. Appl. Anal., 2012 (2012), 1-10
##[13]
L. Cădariu, V. Radu, Fixed points and the stability of Jensen's functional equation, J. Inequal. Pure Appl. Math., 4 (2003), 1-7
##[14]
L. S. Chadli, S. Melliani, A. Moujahid, M. Elomari, Generalized solution of Sine-Gordon equation, Int. J. Nonlinear Anal. Appl., 7 (2016), 87-92
##[15]
I. S. Chang, M. Eshaghi Gordji, H. Khodaei, H. M. Kim, Nearly quartic mappings in \(\beta\)-homogeneous F-spaces, Results Math., 63 (2013), 529-541
##[16]
S. C. Cheng, J. N. Mordeson, Fuzzy linear operators and fuzzy normed linear spaces, Bull. Calcutta Math. Soc., 86 (1994), 429-436
##[17]
K. Ciepliński, Applications of fixed point theorems to the Hyers-Ulam stability of functional equations-a survey, Ann. Funct. Anal., 3 (2012), 151-164
##[18]
J. B. Diaz, B. Margolis, A fixed point theorem of the alternative, for contractions on a generalized complete metric space, Bull. Amer. Math. Soc., 74 (1968), 305-309
##[19]
M. Eshaghi Gordji, H. Khodaei, T. M. Rassias, R. Khodabakhsh, \(J^*\)-homomorphisms and \(J^*\)-derivations on \(J^*\)-algebras for a generalized Jensen type functional equation, Fixed Point Theory, 13 (2012), 481-494
##[20]
C. Felbin, Finite-dimensional fuzzy normed linear space, Fuzzy Sets and Systems, 48 (1992), 239-248
##[21]
P. Găvruţa, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl., 184 (1994), 431-436
##[22]
D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U. S. A, 27 (1941), 222-224
##[23]
D. H. Hyers, G. Isac, T. M. Rassias, Stability of functional equations in several variables, Progress in Nonlinear Differential Equations and their Applications, Birkhäuser Boston, Inc., Boston (1998)
##[24]
G. Isac, T. M. Rassias, On the Hyers-Ulam stability of \(\psi\) -additive mappings, J. Approx. Theory, 72 (1993), 131-137
##[25]
W. Jabłoński, Sum of graphs of continuous functions and boundedness of additive operators, J. Math. Anal. Appl., 312 (2005), 527-534
##[26]
S.-M. Jung, Hyers-Ulam-Rassias stability of functional equations in nonlinear analysis, Springer Optimization and Its Applications, Springer, New York (2011)
##[27]
A. K. Katsaras, Fuzzy topological vector spaces, II, Fuzzy Sets and Systems, 12 (1984), 143-154
##[28]
H. Khodaei, R. Khodabakhsh, M. Eshaghi Gordji, Fixed points, Lie \(*\)-homomorphisms and Lie \(*\)-derivations on Lie \(C^*\)-algebras, Fixed Point Theory, 14 (2013), 387-400
##[29]
I. Kramosil, J. Michálek, Fuzzy metrics and statistical metric spaces, Kybernetika (Prague), 11 (1975), 336-344
##[30]
S. V. Krishna, K. K. M. Sarma, Separation of fuzzy normed linear spaces, Fuzzy Sets and Systems, 63 (1994), 207-217
##[31]
G. Lu, C. K. Park, Hyers-Ulam stability of additive set-valued functional equations, Appl. Math. Lett., 24 (2011), 1312-1316
##[32]
D. Mihet, V. Radu, On the stability of the additive Cauchy functional equation in random normed spaces, J. Math. Anal. Appl., 343 (2008), 567-572
##[33]
F. Moradlou, M. Eshaghi Gordji, Approximate Jordan derivations on Hilbert \(C^*\)-modules, Fixed Point Theory, 14 (2013), 413-425
##[34]
C.-G. Park, Homomorphisms between Poisson \(JC^*\)-algebras, Bull. Braz. Math. Soc. (N.S.), 36 (2005), 79-97
##[35]
C. K. Park, Fixed points and Hyers-Ulam-Rassias stability of Cauchy-Jensen functional equations in Banach algebras, Fixed Point Theory Appl., 2007 (2007), 1-15
##[36]
C. K. Park, K. Ghasemi, S. Ghaffary Ghaleh, Fuzzy n-Jordan \(*\)-derivations on induced fuzzy \(C^*\)-algebras, J. Comput. Anal. Appl., 16 (2014), 494-502
##[37]
C. K. Park, S. O. Kim, J. R. Lee, D. Y. Shin, Quadratic \(\rho\)-functional inequalities in \(\beta\)-homogeneous normed spaces, Int. J. Nonlinear Anal. Appl., 6 (2015), 21-26
##[38]
C. Park, A. Najati, Generalized additive functional inequalities in Banach algebras, Int. J. Nonlinear Anal. Appl., 1 (2010), 54-62
##[39]
C. Park, J. M. Rassias, Stability of the Jensen-type functional equation in \(C^*\)-algebras: a fixed point approach, Abstr. Appl. Anal., 2009 (2009), 1-17
##[40]
T. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72 (1978), 297-300
##[41]
T. M. Rassias, Functional equations and inequalities, Mathematics and its Applications, Kluwer Academic Publishers, Dordrecht (2000)
##[42]
T. M. Rassias, On the stability of functional equations and a problem of Ulam, Acta Math. Appl., 62 (2000), 23-130
##[43]
T. M. Rassias, On the stability of functional equations in Banach spaces, J. Math. Anal. Appl., 251 (2000), 264-284
##[44]
R. Saadati, S. M. Vaezpour, Some results on fuzzy Banach spaces, J. Appl. Math. Comput., 17 (2005), 475-484
##[45]
B.-S. Shieh, Infinite fuzzy relation equations with continuous t-norms, Inform. Sci., 2008 (178), 1961-1967
##[46]
S. M. Ulam, Problems in modern mathematics, Wiley,, New York (1960)
##[47]
C. X. Wu, J. X. Fang, Fuzzy generalization of Klomogoroffs theorem, J. Harbin Inst. Technol., 1 (1984), 1-7
##[48]
J.-Z. Xiao, X.-H. Zhu, Fuzzy normed space of operators and its completeness, Fuzzy Sets and Systems, 133 (2003), 389-399
]
Iterative algorithms for finding minimum-norm fixed point of a finite family of nonexpansive mappings and applications
Iterative algorithms for finding minimum-norm fixed point of a finite family of nonexpansive mappings and applications
en
en
This paper deals with iterative methods for approximating the minimum-norm common fixed point of
nonexpansive mappings. The proposed cyclic iterative algorithms and simultaneous iterative algorithms
combined with a relaxation factor, which make them more
flexible to solve the considered problem. Under
certain conditions on the parameters, we prove that the sequences generated by the proposed iteration
scheme converge strongly to the minimum-norm common fixed point of a finite family of nonexpansive
mappings. Furthermore, as applications, we obtain several new strong convergence theorems for solving
the multiple-set split feasibility problem which has been found application in intensity modulated radiation
therapy. Our results extend and improve some known results in the literature.
5980
5994
Yuchao
Tang
Department of Mathematics
Nanchang University
P. R. China
hhaaoo1331@163.com
Chunxiang
Zong
Department of Mathematics
Nanchang University
P. R. China
2295358036@qq.com
Common fixed point
nonexpansive mappings
minimum-norm
cyclic iteration method
simultaneous iteration method.
Article.6.pdf
[
[1]
F. E. Browder, Convergence theorems for sequences of nonlinear operators in Banach spaces, Math. Z., 100 (1967), 201-225
##[2]
R. E. Bruck, Jr., Properties of fixed-point sets of nonexpansive mappings in Banach spaces, Trans. Amer. Math. Soc., 179 (1973), 251-262
##[3]
C. Byrne, A unified treatment of some iterative algorithms in signal processing and image reconstruction, Inverse Problems, 20 (2004), 103-120
##[4]
Y. Cai, Y. C. Tang, L. W. Liu, Iterative algorithms for minimum-norm fixed point of non-expansive mapping in Hilbert space, Fixed Point Theory Appl., 2012 (2012), 1-10
##[5]
Y. Censor, T. Elfving, N. Kopf, T. Bortfeld, The multiple-sets split feasibility problem and its applications for inverse problems, Inverse Problems, 21 (2005), 2071-2084
##[6]
C. E. Chidume, C. O. Chidume, Iterative approximation of fixed points of nonexpansive mappings, J. Math. Anal. Appl., 318 (2006), 288-295
##[7]
P. L. Combettes, The convex feasibility problem in image recovery, Adv. Imag. Elect. Phys., 95 (1996), 155-270
##[8]
Y.-L. Cui, X. Liu, Notes on Browder's and Halpern's methods for nonexpansive mappings, Fixed Point Theory, 10 (2009), 89-98
##[9]
B. Halpern, Fixed points of nonexpanding maps, Bull. Amer. Math. Soc., 73 (1967), 957-961
##[10]
H. M. He, S. Y. Liu, M. A. Noor, Some Krasnonselski-Mann algorithms and the multiple-set split feasibility problem, Fixed Point Theory Appl., 2010 (2010), 1-12
##[11]
X. Liu, Y. L. Cui, The common minimal-norm fixed point of a finite family of nonexpansive mappings, Nonlinear Anal., 73 (2010), 76-83
##[12]
X. Liu, Y. L. Cui, Minimum-norm fixed point of nonexpansive nonself mappings in Hilbert spaces, Fixed Point Theory,, 13 (2012), 129-136
##[13]
P. E. Maingé, Regularized and inertial algorithms for common fixed points of nonlinear operators, J. Math. Anal. Appl., 344 (2008), 876-887
##[14]
Y. S. Song, K. Promluang, P. Kumam, Y. J. Cho, Some convergence theorems of the Mann iteration for monotone \(\alpha\)-nonexpansive mappings, Appl. Math. Comput., 287/288 (2016), 74-82
##[15]
S. Suantai, P. Cholamjiak, Y. J. Cho, W. Cholamjiak, On solving split equilibrium problems and fixed point problems of nonspreading multi-valued mappings in Hilbert spaces, Fixed Point Theory Appl., 2016 (2016), 1-16
##[16]
P. Sunthrayuth, Y. J. Cho, P. Kumam, General iterative algorithms approachto variational inequalities and minimum-norm fixed point for minimization and split feasibility problems, OPSEARCH, 51 (2014), 400-415
##[17]
T. Suzuki, Strong convergence of Krasnoselskii and Mann's type sequences for one-parameter nonexpansive semi- groups without Bochner integrals, J. Math. Anal. Appl., 305 (2005), 227-239
##[18]
T. Suzuki, A sufficient and necessary condition for Halpern-type strong convergence to fixed points of nonexpansive mappings, Proc. Amer. Math. Soc., 135 (2007), 99-106
##[19]
T. Suzuki, Some notes on Bauschke's condition, Nonlinear Anal., 67 (2007), 2224-2231
##[20]
Y. C. Tang, Y. Cai, L. W. Liu, Approximation to minimum-norm common fixed point of a semigroup of nonexpansive operators, Math. Commun., 18 (2013), 87-96
##[21]
Y. C. Tang, L. W. Liu, Iterative algorithms for finding minimum-norm fixed point of nonexpansive mappings and applications, Math. Methods Appl. Sci., 37 (2014), 1137-1146
##[22]
H.-K. Xu, Iterative algorithms for nonlinear operators, J. London Math. Soc., 66 (2002), 240-256
##[23]
H.-K. Xu, A variable Krasnoselskiĭ-Mann algorithm and the multiple-set split feasibility problem, Inverse problems, 22 (2006), 2021-2034
##[24]
I. Yamada, N. Ogura, Hybrid steepest descent method for variational inequality problem over the fixed point set of certain quasi-nonexpansive mappings, Numer. Funct. Anal. Optim., 25 (2004), 619-655
##[25]
X. Yang, Y.-C. Liou, Y. H. Yao, Finding minimum norm fixed point of nonexpansive mappings and applications, Math. Probl. Eng., 2011 (2011), 1-13
##[26]
Y. H. Yao, Y.-C. Liou, Some unified algorithms for finding minimum norm fixed point of nonexpansive semigroups in Hilbert spaces, An. Ştiinţ. Univ., (), -
##[27]
Y. H. Yao, Y.-C. Liou, N. Shahzad, Iterative methods for nonexpansive mappings in Banach spaces, Numer. Func. Anal. Optim., 32 (2011), 583-592
##[28]
Y. H. Yao, H.-K. Xu, Iterative methods for finding minimum-norm fixed points of nonexpansive mappings with applications, Optimization, 60 (2011), 645-658
##[29]
X. Yu, N. Shahzad, Y. H. Yao, Implicit and explicit algorithms for solving the split feasibility problem, Optim. Lett., 6 (2012), 1447-1462
##[30]
H. Zegeye, N. Shahzad, Approximation of the common minimum-norm fixed point of a finite family of asymptotically nonexpansive mappings, Fixed Point Theory Appl., 2013 (2013), 1-12
##[31]
H. Zegeye, N. Shahzad, M. A. Alghamdi, Minimum-norm fixed point of pseudocontractive mappings, Abstr. Appl. Anal., 2012 (2012), 1-15
]
3-variable Jensen \(\rho\)-functional inequalities and equations
3-variable Jensen \(\rho\)-functional inequalities and equations
en
en
In this paper, we introduce and investigate Jensen \(\rho\)-functional inequalities associated with the following
Jensen functional equations
\[f(x + y + z) + f(x + y - z) - 2f(x) - 2f(y) = 0,\\
f(x + y + z) - f(x - y - z) - 2f(y) - 2f(z) = 0.\]
We prove the Hyers-Ulam-Rassias stability of the Jensen \(\rho\)-functional inequalities in complex Banach spaces
and prove the Hyers-Ulam-Rassias stability of the Jensen \(\rho\)-functional equations associated with the \(\rho\)-
functional inequalities in complex Banach spaces.
5995
6003
Gang
Lu
Department of Mathematics, School of Science
Shenyang University of Technology
P. R. China
lvgang1234@hanmail.net
Qi
Liu
Department of Mathematics, School of Science
Shenyang University of Technology
P. R. China
903037649@qq.com
Yuanfeng
Jin
Department of Mathematics
Yanbian University
P. R. China
yfjim@ybu.edu.cn
Jun
Xie
Department of Mathematics, School of Science
Shenyang University of Technology
P. R. China
583193617@qq.com
Jensen functional inequalities
Hyers-Ulam-Rassias stability
complex Banach spaces.
Article.7.pdf
[
[1]
T. Aoki, On the stability of the linear transformation in Banach spaces, J. Math. Soc. Japan, 2 (1950), 64-66
##[2]
J. Aczél, J. Dhombres, Functional equations in several variables, With applications to mathematics, information theory and to the natural and social sciences, Encyclopedia of Mathematics and its Applications, Cambridge University Press, Cambridge (1989)
##[3]
L. Cădariu, V. Radu, Fixed points and the stability of Jensen's functional equation, JIPAM. J. Inequal. Pure Appl. Math., 4 (2003), 1-7
##[4]
I. S. Chang, M. Eshaghi Gordji, H. Khodaei, H. M. Kim, Nearly quartic mappings in \(\beta\)-homogeneous F-spaces, Results Math., 63 (2013), 529-541
##[5]
Y. J. Cho, C. K. Park, R. Saadati, Functional inequalities in non-Archimedean Banach spaces, Appl. Math. Lett., 23 (2010), 1238-1242
##[6]
Y. J. Cho, R. Saadati, Y.-O. Yang, Approximation of homomorphisms and derivations on Lie \(C^*\)-algebras via fixed point method, J. Inequal. Appl., 2013 (2013), 1-9
##[7]
P. W. Cholewa, Remarks on the stability of functional equations, Aequationes Math., 27 (1984), 76-86
##[8]
J. B. Diaz, B. Margolis, A fixed point theorem of the alternative, for contractions on a generalized complete metric space, Bull. Amer. Math. Soc., 74 (1968), 305-309
##[9]
A. Ebadian, N. Ghobadipour, T. M. Rassias, M. Eshaghi Gordji, Functional inequalities associated with Cauchy additive functional equation in non-Archimedean spaces, Discrete Dyn. Nat. Soc., 2011 (2011), 1-14
##[10]
P. Găvruţa, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl., 184 (1994), 431-436
##[11]
D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U. S. A., 27 (1941), 222-224
##[12]
D. H. Hyers, G. Isac, T. M. Rassias, Stability of functional equations in several variables, Progress in Nonlinear Differential Equations and their Applications, Birkhäuser Boston, Inc., Boston (1998)
##[13]
G. Isac, T. M. Rassias, On the Hyers-Ulam stability of \(\psi\)-additive mappings, J. Approx. Theory, 72 (1993), 131-137
##[14]
V. Lakshmikantham, S. Leela, J. Vasundhara Devi, Theory of fractional dynamic systems, Cambridge Scientific Publishers, (2009)
##[15]
S.-B. Lee, J.-H. Bae, W.-G. Park, On the stability of an additive functional inequality for the fixed point alternative, J. Comput. Anal. Appl., 17 (2014), 361-371
##[16]
G. Lu, C. K. Park, Hyers-Ulam Stability of Additive Set-valued Functional Equations, Appl. Math. Lett., 24 (2011), 1312-1316
##[17]
C. K. Park, Y. S. Cho, M.-H. Han, Functional inequalities associated with Jordan-von Neumann-type additive functional equations, J. Inequal. Appl., 2007 (2007), 1-13
##[18]
T. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72 (1978), 297-300
##[19]
J. M. Rassias, On approximation of approximately linear mappings by linear mappings, J. Funct. Anal., 46 (1982), 126-130
##[20]
J. M. Rassias, On approximation of approximately linear mappings by linear mappings, Bull. Sci. Math., 108 (1984), 445-446
##[21]
J. M. Rassias, Solution of a problem of Ulam, J. Approx. Theory, 57 (1989), 268-273
##[22]
J. M. Rassias, Complete solution of the multi-dimensional problem of Ulam, Discuss. Math., 14 (1994), 101-107
##[23]
T. M. Rassias, Functional equations and inequalities, Mathematics and its Applications, Kluwer Academic Publishers, Dordrecht (2000)
##[24]
T. M. Rassias, On the stability of functional equations and a problem of Ulam, Acta Math. Appl., 62 (2000), 23-130
##[25]
T. M. Rassias, On the stability of functional equations in Banach spaces, J. Math. Anal. Appl., 251 (2000), 264-284
##[26]
J. M. Rassias, Refined Hyers-Ulam approximation of approximately Jensen type mappings, Bull. Sci. Math., 131 (2007), 89-98
##[27]
J. M. Rassias, M. J. Rassias, On the Ulam stability of Jensen and Jensen type mappings on restricted domains, J. Math. Anal. Appl., 281 (2003), 516-524
##[28]
S. M. Ulam, Problems in modern mathematics (Chapter VI), Wiley,, New York (1960)
##[29]
T. Z. Xu, J. M. Rassias, W. X. Xu,, A fixed point approach to the stability of a general mixed additive-cubic functional equation in quasi fuzzy normed spaces, Int. J. Phys. Sci., 6 (2011), 313-324
]
On properties of solutions to the improved modified Boussinesq equation
On properties of solutions to the improved modified Boussinesq equation
en
en
In this paper, we investigate the Cauchy problem for the generalized IBq equation with damping in
one dimensional space. When \(\sigma = 1\), the nonlinear approximation of the global solutions is established
under small condition on the initial value. Moreover, we show that as time tends to infinity, the solution is
asymptotic to the superposition of nonlinear diffusion waves which are given explicitly in terms of the selfsimilar
solution of the viscous Burgers equation. When \(\sigma\geq 2\), we prove that our global solution converges
to the superposition of diffusion waves which are given explicitly in terms of the solution of linear parabolic
equation.
6004
6020
Yuzhu
Wang
School of Mathematics and Information Sciences
North China University of Water Resources and Electric Power
China
wangyuzhu@ncwu.edu.cn
Yinxia
Wang
School of Mathematics and Information Sciences
North China University of Water Resources and Electric Power
China
yinxia117@126.com
IMBq equation with damping
large time behavior
diffusion waves.
Article.8.pdf
[
[1]
E. Arévalo, Y. Gaididei, F. G. Mertens, Soliton dynamics in damped and forced Boussinesq equations, Eur. Phys. J. B, 27 (2002), 63-74
##[2]
J. Boussinesq, Théorie des ondes et des remous qui se propagent le long d'un canal rectangulaire horizontal en communiquant au liquide contenu dans ce canal des vitesses sensiblement pareilles de la surface au fond, (French) [Theory of waves and vortices propagating along a horizontal rectanglar channel, communicating to the liquid in the channel generally similar velocities of the bottom surface], J. Math. Pures Appl., 17 (1872), 55-108
##[3]
J. Boussinesq, Essai sur la théorie des eaux courantes, memo presented at the Acadmic des Sciences Inst. France (series), 23 (1877), 1-680
##[4]
Y. G. Cho, T. Ozawa, On small amplitude solutions to the generalized Boussinesq equations, Discrete Contin. Dyn. Syst., 17 (2007), 691-711
##[5]
M. Kato, Large time behavior of solutions to the generalized Burgers equations, Osaka J. Math., 44 (2007), 923-943
##[6]
M. Kato, Y.-Z. Wang, S. Kawashima, Asymptotic behavior of solutions to the generalized cubic double dispersion equation in one space dimension, Kinet. Relat. Models, 6 (2013), 969-987
##[7]
S. Kawashima, Large-time behaviour of solutions to hyperbolic-parabolic systems of conservation laws and applications, Proc. Roy. Soc. Edinburgh Sect. A, 106 (1987), 169-194
##[8]
S. Kawashima, Y.-Z. Wang, Global existence and asymptotic behavior of solutions to the generalized cubic double dispersion equation, Anal. Appl. (Singap.), 13 (2015), 233-254
##[9]
T. T. Li, Y. M. Chen, Nonlinear evolution equations (Chinese), Science Press, (1989)
##[10]
T.-P. Liu, Hyperbolic and viscous conservation laws, CBMS-NSF Regional Conference Series in Applied Mathematics, Society for Industrial and Applied Mathematics (SIAM), Philadelphia (2000)
##[11]
V. G. Makhankov, Dynamics of classical solitons (in nonintegrable systems), Phys. Rep., 35 (1978), 1-128
##[12]
M. O. Ogundiran, Continuous selections of solution sets of quantum stochastic evolution inclusions, J. Nonlinear Funct. Anal., 2014 (2014), 1-14
##[13]
N. Polat, Existence and blow up of solution of Cauchy problem of the generalized damped multidimensional improved modified Boussinesq equation, Z. Naturforsch A, 63 (2008), 543-552
##[14]
P. Rosenau, Dynamics of nonlinear mass-spring chains near the continuum limit, Phys. Lett. A, 118 (1986), 222-227
##[15]
P. Rosenau, Dynamics of dense lattices, Phys. Rev. B, 36 (1987), 5868-5876
##[16]
Y. X. Wang, Existence and asymptotic behavior of solutions to the generalized damped Boussinesq equation, Electron. J. Differential Equations, 2012 (2012), 1-11
##[17]
Y. X. Wang, Asymptotic decay estimate of solutions to the generalized damped \(B_q\) equation, J. Inequal. Appl., 2013 (2013), 1-12
##[18]
Y. X. Wang, On the Cauchy problem for one dimension generalized Boussinesq equation, Internat. J. Math., 26 (2015), 1-22
##[19]
S. B. Wang, G. W. Chen, Small amplitude solutions of the generalized IMBq equation, J. Math. Anal. Appl., 274 (2002), 846-866
##[20]
S. B. Wang, G. W. Chen, The Cauchy problem for the generalized IMBq equation in \(W_{s;p}(R^n)\), J. Math. Anal. Appl., 266 (2002), 38-54
##[21]
Y.-Z. Wang, S. Chen, Asymptotic profile of solutions to the double dispersion equation, Nonlinear Anal., 134 (2016), 236-254
##[22]
Y.-Z. Wang, K. Y. Wang, Decay estimate of solutions to the sixth order damped Boussinesq equation, Appl. Math. Comput., 239 (2014), 171-179
##[23]
S. B.Wang, H. Y. Xu, On the asymptotic behavior of solution for the generalized IBq equation with hydrodynamical damped term, J. Differential Equations, 252 (2012), 4243-4258
##[24]
Y. Z. Zhang, P. F. Li, Decay estimates of solutions to the IBq equation, Bulletin of the Iranian Mathematical Society, ((to appear)), -
##[25]
S. M. Zheng, Nonlinear evolution equations, Chapman & Hall/CRC Monographs and Surveys in Pure and Applied Mathematics, Chapman & Hall/CRC, Boca Raton (2004)
]
Frozen jacobian iterative method for solving systems of nonlinear equations application to nonlinear IVPs and BVPs
Frozen jacobian iterative method for solving systems of nonlinear equations application to nonlinear IVPs and BVPs
en
en
Frozen Jacobian iterative methods are of practical interest to solve the system of nonlinear equations. A
frozen Jacobian multi-step iterative method is presented. We divide the multi-step iterative method into two
parts namely base method and multi-step part. The convergence order of the constructed frozen Jacobian
iterative method is three, and we design the base method in a way that we can maximize the convergence
order in the multi-step part. In the multi-step part, we utilize a single evaluation of the function, solve four
systems of lower and upper triangular systems and a second frozen Jacobian. The attained convergence
order per multi-step is four. Hence, the general formula for the convergence order is \(3 + 4(m - 2)\) for
\(m \geq 2\) and \(m\) is the number of multi-steps. In a single instance of the iterative method, we employ only
single inversion of the Jacobian in the form of LU factors that makes the method computationally cheaper
because the LU factors are used to solve four system of lower and upper triangular systems repeatedly. The
claimed convergence order is verified by computing the computational order of convergence for a system of
nonlinear equations. The efficiency and validity of the proposed iterative method are narrated by solving
many nonlinear initial and boundary value problems.
6021
6033
Malik Zaka
Ullah
Department of Mathematics, Faculty of Science
Dipartimento di Scienza e Alta Tecnologia
King Abdulaziz University
Universita dell'Insubria
Saudi Arabia
Italy
mzhussain@kau.edu.sa;malik.zakaullah@uninsubria.it
Fayyaz
Ahmad
Dipartimento di Scienza e Alta Tecnologia
Departament de Fisica i Enginyeria Nuclear
Universita dell'Insubria
Universitat Politecnica de Catalunya
UCERD Islamabad
Italy
Spain
Pakistan
Ali Saleh
Alshomrani
Department of Mathematics, Faculty of Science
King Abdulaziz University
Saudi Arabia
A. K.
Alzahrani
Department of Mathematics, Faculty of Science
King Abdulaziz University
Saudi Arabia
Metib Said
Alghamdi
Mathematics Department, Faculty of science
Jazan University
Saudi Arabia
Shamshad
Ahmad
Department of Heat and Mass Transfer Technological Center
Technical University of Catalonia
Spain
Shahid
Ahmad
Department of Mathematics
Government College University Lahore
Pakistan
Frozen Jacobian iterative methods
multi-step iterative methods
systems of nonlinear equations
nonlinear initial value problems
nonlinear boundary value problems.
Article.9.pdf
[
[1]
F. Ahmad, E. Tohidi, J. A. Carrasco, A parameterized multi-step Newton method for solving systems of nonlinear equations, Numer. Algorithms, 71 (2016), 631-653
##[2]
F. Ahmad, E. Tohidi, M. Z. Ullah, J. A. Carrasco, Higher order multi-step Jarratt-like method for solving systems of nonlinear equations: application to PDEs and ODEs, Comput. Math. Appl., 70 (2015), 624-636
##[3]
E. S. Alaidarous, M. Z. Ullah, F. Ahmad, A. S. Al-Fhaid, An efficient higher-order quasilinearization method for solving nonlinear BVPs, J. Appl. Math., 2013 (2013), 1-11
##[4]
A. H. Bhrawy, An efficient Jacobi pseudospectral approximation for nonlinear complex generalized Zakharov system, Appl. Math. Comput., 247 (2014), 30-46
##[5]
W. H. Bi, H. M. Ren, Q. B. Wu, Three-step iterative methods with eighth-order convergence for solving nonlinear equations, J. Comput. Appl. Math., 225 (2009), 105-112
##[6]
A. Cordero, J. L. Hueso, E. Martínez, J. R. Torregrosa, A modified Newton-Jarratt's composition, Numer. Algorithms, 55 (2010), 87-99
##[7]
M. Davies, B. Dawson, On the global convergence of Halley's iteration formula, Numer. Math., 24 (1975), 133-135
##[8]
M. Dehghan, F. Fakhar-Izadi, The spectral collocation method with three different bases for solving a nonlinear partial differential equation arising in modeling of nonlinear waves, Math. Comput. Modelling, 53 (2011), 1865-1877
##[9]
Y. H. Geum, Y. I. Kim, A multi-parameter family of three-step eighth-order iterative methods locating a simple root, Appl. Math. Comput., 215 (2010), 3375-3382
##[10]
E. Halley,, A new exact and easy method of finding the roots of equations generally and without any previous reduction, Philos. Trans. Roy. Soc. London, 18 (1964), 136-148
##[11]
H. T. Kung, J. F. Traub, Optimal order of one-point and multipoint iteration, J. Assoc. Comput. Mach., 21 (1974), 643-651
##[12]
H. Montazeri, F. Soleymani, S. Shateyi, S. S. Motsa, On a new method for computing the numerical solution of systems of nonlinear equations, J. Appl. Math., 2012 (2012), 1-15
##[13]
F. Soleymani, On a new class of optimal eighth-order derivative-free methods, Acta Univ. Sapientiae Math., 3 (2011), 169-180
##[14]
F. Soleymani, T. Lotfi, P. Bakhtiari, A multi-step class of iterative methods for nonlinear systems, Optim. Lett., 8 (2014), 1001-1015
##[15]
E. Tohidi, S. Lotfi Noghabi, An efficient Legendre pseudospectral method for solving nonlinear quasi bang-bang optimal control problems, J. Appl. Math. Stat. Inform., 8 (2012), 73-84
##[16]
M. Z. Ullah, A. S. Al-Fhaid, F. Ahmad, Four-point optimal sixteenth-order iterative method for solving nonlinear equations, J. Appl. Math., 2013 (2013), 1-5
##[17]
M. Z. Ullah, S. Serra-Capizzano, F. Ahmad, An efficient multi-step iterative method for computing the numerical solution of systems of nonlinear equations associated with ODEs, Appl. Math. Comput., 250 (2015), 249-259
##[18]
M. Z. Ullah, F. Soleymani, A. S. Al-Fhaid, Numerical solution of nonlinear systems by a general class of iterative methods with application to nonlinear PDEs, Numer. Algorithms, 67 (2014), 223-242
##[19]
X. Wang, L. P. Liu, Modified Ostrowski's method with eighth-order convergence and high efficiency index, Appl. Math. Lett., 23 (2010), 549-554
]
Brunn-Minkowski type inequalities for \(L_p\) Blaschke- Minkowski homomorphisms
Brunn-Minkowski type inequalities for \(L_p\) Blaschke- Minkowski homomorphisms
en
en
In this paper, the Brunn-Minkowski type inequalities for \(L_p\) Blaschke-Minkowski homomorphisms and
\(L_p\) radial Minkowski homomorphisms are established.
6034
6040
Feixiang
Chen
Department of Mathematics
School of Mathematics and Statistics
Shanghai University
Chongqing Three Gorges University
China
China
cfx2002@126.com
Gangsong
Leng
Department of Mathematics
Shanghai University
China
gleng@staff.shu.edu.cn
Brunn-Minkowski inequality
\(L_p\) Blaschke-Minkowski homomorphisms
Article.10.pdf
[
[1]
J. Abardia, A. Bernig, Projection bodies in complex vector spaces, Adv. Math., 227 (2011), 830-846
##[2]
J. Abardia, T. Wannerer, Aleksandrov-Fenchel inequalities for unitary valuations of degree 2 and 3, Calc. Var. Partial Differential Equations, 54 (2015), 1767-1791
##[3]
S. Alesker, A. Bernig, F. E. Schuster, Harmonic analysis of translation invariant valuations, Geom. Funct. Anal., 21 (2011), 751-773
##[4]
A. Berg, L. Parapatits, F. E. Schuster, M. Weberndorfer, Log-concavity properties of Minkowski valuations, arXiv, 2014 (2014), 1-44
##[5]
R. J. Gardner, The Brunn-Minkowski inequality, Bull. Amer. Math. Soc. (N.S.), 39 (2002), 355-405
##[6]
R. J. Gardner, Geometric tomography, Second edition, Encyclopedia of Mathematics and its Applications, Cambridge University Press, New York (2006)
##[7]
R. J. Gardner, P. Gronchi, A Brunn-Minkowski inequality for the integer lattice, Trans. Amer. Math. Soc., 353 (2001), 3995-4024
##[8]
R. J. Gardner, D. Hug, W. Weil, Operations between sets in geometry, J. Eur. Math. Soc. (JEMS), 15 (2013), 2297-2352
##[9]
R. J. Gardner, L. Parapatits, F. E. Schuster, A characterization of Blaschke addition, Adv. Math., 254 (2014), 396-418
##[10]
C. Haberl, \(L_p\) intersection bodies, Adv. Math., 217 (2008), 2599-2624
##[11]
F.-H. Lu, G.-S. Leng, On \(L_p\)-Brunn-Minkowski type inequalities of convex bodies, Bol. Soc. Mat. Mexicana, 13 (2007), 167-176
##[12]
M. Ludwig, Projection bodies and valuations, Adv. Math., 172 (2002), 158-168
##[13]
M. Ludwig, Intersection bodies and valuations, Amer. J. Math., 128 (2006), 1409-1428
##[14]
E. Lutwak, Inequalities for mixed projection bodies, Trans. Amer. Math. Soc., 339 (1993), 901-916
##[15]
E. Lutwak, The Brunn-Minkowski-Firey theory, I, Mixed volumes and the Minkowski problem, J. Differential Geom., 38 (1993), 131-150
##[16]
R. Osserman, The Brunn-Minkowski inequality for multiplictities, Invent. Math., 125 (1996), 405-411
##[17]
L. Parapatits, F. E. Schuster, The Steiner formula for Minkowski valuations, Adv. Math., 230 (2012), 978-994
##[18]
R. Schneider, Convex bodies: the Brunn-Minkowski theory, Encyclopedia of Mathematics and its Applications, Cambridge University Press, Cambridge (1993)
##[19]
F. E. Schuster, Volume inequalities and additive maps of convex bodies, Mathematika, 53 (2006), 211-234
##[20]
F. E. Schuster, Valuations and Busemann-Petty type problems, Adv. Math., 219 (2008), 344-368
##[21]
F. E. Schuster, Crofton measures and Minkowski valuations, Duke Math. J., 154 (2010), 1-30
##[22]
W. Wang, \(L_p\) Blaschke-Minkowski homomorphisms, J. Inequal. Appl., 2013 (2013), 1-14
##[23]
W. Wang, \(L_p\) Brunn-Minkowski type inequalities for Blaschke-Minkowski homomorphisms, Geom. Dedicata, 164 (2013), 273-285
##[24]
W. Wang, L.-J. Liu, B.-W. He, \(L_p\) radial Minkowski homomorphisms, Taiwanese J. Math., 15 (2011), 1183-1199
##[25]
T. Wannerer, GL(n) equivariant Minkowski valuations, Indiana Univ. Math. J., 60 (2011), 1655-1672
]
Properties and application of smooth function germs of orbit tangent space
Properties and application of smooth function germs of orbit tangent space
en
en
The finite determinacy of smooth function germ is the key in approximating the nonlinear function with
infinite terms by its finite terms. In this paper, we discuss the inclusion relations with a new equivalent form
for function germs in orbit tangent spaces, and get an improved form of the finite \(k\)-determinacy of smooth
function germ. As an application, the methods in judging the right equivalency of Whitney function family
with codimension 8 are presented.
6041
6047
Wenliang
Gan
School of Mathematics and Statistics
Northeast Normal University
P. R. China
ganwl947@nenu.edu.cn
Donghe
Pei
School of Mathematics and Statistics
Northeast Normal University
P. R. China
peidh340@nenu.edu.cn
Qiang
Li
School of Science
Qiqihar University
P. R. China
liq347@nenu.edu.cn
Diffeomorphism
function germ
Jacobian ideal
\(\mathcal{R}\)-equivalence.
Article.11.pdf
[
[1]
L. Kushner, B. Terra Leme, Finite relative determination and relative stability, Pacific J. Math., 192 (2000), 315-328
##[2]
Y. Li, W. He, Versal unfolding of equivariant bifurcation problems in more general case under two equivalent groups, Acta Math. Sci. Ser. B Engl. Ed., 28 (2008), 915-923
##[3]
J. Martinet, Singularities of smooth functions and maps, Cambridge University Press, Cambridge-New York (1982)
##[4]
J. N. Mather, Stability of \(C^\infty\) mapping, III: Finitely determined map germs, Publ. Math I. H. E. S., 35 (1969), 127-156
##[5]
C. Shi, D. Pei, Weak finite determinacy of relative map germs, Chin. Ann. Math. Ser. B, 35 (2014), 991-1000
##[6]
B. Sun, L. C. Wilson, Determinacy of smooth germs with real isolated line singularities, Proc. Amer. Math. Soc., 129 (2001), 2789-2797
##[7]
C. T. C. Wall, Determinacy of smooth map-germs, Bull. London Math. Soc., 13 (1981), 481-539
##[8]
J. C. Zou, Finite determination and universal unfoldings of bifurcation problems, Acta Math. Sinica (N. S.), 14 (1998), 663-674
]
Positive solutions of an integral boundary value problem for singular differential equations of mixed type with \(p\)-Laplacian
Positive solutions of an integral boundary value problem for singular differential equations of mixed type with \(p\)-Laplacian
en
en
In this paper, by Leggett-William fixed point theorem, we establish the existence of triple positive
solutions of a new kind of integral boundary value problem for the nonlinear singular differential equations
with \(p\)-Laplacian operator, in which \(q(t)\) can be singular at \(t = 0; 1\). We also show that the results obtained
can be applied to study certain higher order mixed boundary value problems. At last, we give an example
to demonstrate the use of the main result of this paper. The conclusions in this paper essentially extend
and improve the known results.
6048
6057
Changlong
Yu
College of Sciences
Hebei University of Science and Technology
P. R. China
changlongyu@126.com
Jufang
Wang
College of Sciences
Hebei University of Science and Technology
P. R. China
wangjufang1981@126.com
Yanping
Guo
College of Sciences
Hebei University of Science and Technology
P. R. China
guoyanping65@126.com
Positive solutions
integral boundary value problem
Leggett-William fixed point theorem
p-Laplacian operator
cone.
Article.12.pdf
[
[1]
N. Al Arifi, I. Altun, M. Jleli, A. Lashin, B. Samet, Lyapunov-type inequalities for a fractional p-Laplacian equation, J. Inequal. Appl., 2016 (2016), 1-11
##[2]
H.-Y. Feng, W.-G. Ge, Existence of three positive solutions for m-point boundary-value problems with one- dimensional p-Laplacian, Nonlinear Anal., 68 (2008), 2017-2026
##[3]
Y.-P. Guo, C.-L. Yu, J.-F. Wang,, Existence of three positive solutions for m-point boundary value problems on infinite intervals, Nonlinear Anal., 71 (2009), 717-722
##[4]
X.-M. He, W.-G. Ge, Triple solutions for second-order three-point boundary value problems, J. Math. Anal. Appl., 268 (2002), 256-265
##[5]
X.-M. He, W.-G. Ge, Twin positive solutions for the one-dimensional p-Laplacian boundary value problems, Nonlinear Anal., 56 (2004), 975-984
##[6]
X.-M. He, W.-G. Ge, M.-S. Peng, Multiple positive solutions for one-dimensional p-Laplacian boundary value problems, Appl. Math. Lett., 15 (2002), 937-943
##[7]
J.-X. Hu, D.-X. Ma, Triple positive solutions of a boundary value problem for second order three-point differential equations with p-Laplacian operator, J. Appl. Math. Comput., 36 (2011), 251-261
##[8]
D. Kong, L.-S. Liu, Y.-H. Wu, Triple positive solutions of a boundary value problem for nonlinear singular second- order differential equations of mixed type with p-Laplacian, Comput. Math. Appl., 58 (2009), 1425-1432
##[9]
L.-B. Kong, J.-Y. Wang, Multiple positive solutions for the one-dimensional p-Laplacian, Nonlinear Anal., 42 (2000), 1327-1333
##[10]
A. Lakmeche, A. Hammoudi, Multiple positive solutions of the one-dimensional p-Laplacian, J. Math. Anal. Appl., 317 (2006), 43-49
##[11]
L.-S. Liu, C.-X. Wu, F. Guo, Existence theorems of global solutions of initial value problems for nonlinear in- tegrodifferential equations of mixed type in Banach spaces and applications, Comput. Math. Appl., 47 (2004), 13-22
##[12]
D.-X. Ma, Existence and iteration of positive solution for a three-point boundary value problem with a p-Laplacian operator,, J. Appl. Math. Comput., 25 (2007), 329-337
##[13]
J.-Y. Wang, The existence of positive solutions for the one-dimensional p-Laplacian, Proc. Amer. Math. Soc., 125 (1997), 2275-2283
##[14]
J.-F. Wang, C.-L. Yu, Y.-P. Guo, Triple positive solutions of a nonlocal boundary value problem for singular differential equations with p-Laplacian, Abstr. Appl. Anal., 2013 (2013), 1-7
##[15]
C.-L. Yu, J.-F. Wang, C.-Y. Zuo, Existence of positive solutions for second-order three-point boundary value problems with p-Laplacian operator, J. Hebei Univ. Sci. Technol., 32 (2014), 127-133
##[16]
D.-X. Zhao, H.-Z. Wang, W.-G. Ge, Existence of triple positive solutions to a class of p-Laplacian boundary value problems, J. Math. Anal. Appl., 328 (2007), 972-983
]
A variant form of Korpelevichs algorithm and its convergence analysis
A variant form of Korpelevichs algorithm and its convergence analysis
en
en
A variant form of Korpelevich's algorithm is presented for solving the generalized variational inequality
in Banach spaces. It is shown that the presented algorithm converges strongly to a special solution of the
generalized variational inequality.
6058
6066
Li-Jun
Zhu
School of Management
School of Mathematics and Information Science
Hefei University of Technology
Beifang University of Nationalities
China
China
zhulijun1995@yahoo.com
Minglun
Ren
School of Management
Hefei University of Technology
China
hfutren@sina.com.cn
Weimin
Han
Department of Mathematics
University of Iowa
U. S. A.
weimin-han@uiowa.edu
Korpelevich's algorithm
variational inequalities
accretive mappings
Banach spaces.
Article.13.pdf
[
[1]
K. Aoyama, H. Iiduka, W. Takahashi, Weak convergence of an iterative sequence for accretive operators in Banach spaces, Fixed Point Theory Appl., 2006 (2006), 1-13
##[2]
J. Y. Bello Cruz, A. N. Iusem, A strongly convergent direct method for monotone variational inequalities in Hilbert spaces, Numer. Funct. Anal. Optim., 30 (2009), 23-36
##[3]
F. E. Browder, Nonlinear operators and nonlinear equations of evolution in Banach spaces,Nonlinear functional analysis, Proc. Sympos. Pure Math., Chicago, Ill., XVIII (1968), 1{308, Amer. Math. Soc., Providence (1976)
##[4]
R. E. Bruck, Nonexpansive retracts of Banach spaces, Bull. Amer. Math. Soc., 76 (1970), 384-386
##[5]
R. Glowinski, Numerical methods for nonlinear variational problems, Springer-Verlag, New York (1984)
##[6]
B.-S. He, Z.-H. Yang, X.-M. Yuan, An approximate proximal-extragradient type method for monotone variational inequalities, J. Math. Anal. Appl., 300 (2004), 362-374
##[7]
A. N. Iusem, B. F. Svaiter, A variant of Korpelevich's method for variational inequalities with a new search strategy, Optimization, 42 (1997), 309-321
##[8]
G. M. Korpelević, An extragradient method for finding saddle points and for other problems, (Russian) Èkonom. i Mat. Metody, 12 (1976), 747-756
##[9]
G. Stampacchi, Formes bilineaires coercivites surles ensembles convexes, CR Acad. Sci. Paris, 258 (1964), 4413-4416
##[10]
W. Takahashi, M. Toyoda, Weak convergence theorems for nonexpansive mappings and monotone mappings, J. Optim. Theory Appl., 118 (2003), 417-428
##[11]
H.-K. Xu, Inequalities in Banach spaces with applications, Nonlinear Anal., 16 (1991), 1127-1138
##[12]
H.-K. Xu, Iterative algorithms for nonlinear operators, J. London Math. Soc., 66 (2002), 240-256
##[13]
H.-K. Xu, T.-H. Kim, Convergence of hybrid steepest-descent methods for variational inequalities, J. Optim. Theory Appl., 119 (2003), 185-201
##[14]
Y.-H. Yao, R.-D. Chen, H.-K. Xu, Schemes for finding minimum-norm solutions of variational inequalities, Nonlinear Anal., 72 (2010), 3447-3456
##[15]
Y.-H. Yao, G, Marino, L. Muglia, A modified Korpelevich's method convergent to the minimum-norm solution of a variational inequality, Optimization, 63 (2014), 559-569
##[16]
Y.-H. Yao, G. Marino, H.-K. Xu, Y.-C. Liou, Construction of minimum-norm fixed points of pseudocontractions in Hilbert spaces, J. Inequal. Appl., 2014 (2014), 1-14
##[17]
Y.-H. Yao, M. A. Noor, Y.-C. Liou, Strong convergence of a modified extragradient method to the minimum-norm solution of variational inequalities, Abstr. Appl. Anal., 2012 (2012), 1-9
##[18]
Y.-H. Yao, M. A. Noor, Y.-C. Liou, S. M. Kang, Iterative algorithms for general multivalued variational inequalities, Abstr. Appl. Anal., 2012 (2012), 1-10
##[19]
Y.-H. Yao, M. Postolache, S. M. Kang, Strong convergence of approximated iterations for asymptotically pseudo- contractive mappings, Fixed Point Theory Appl., 2014 (2014), 1-13
##[20]
Y.-H. Yao, M. Postolache, Y.-C. Liou, Strong convergence of a self-adaptive method for the split feasibility problem, Fixed Point Theory Appl., 2013 (2013), 1-12
]
On certain multivalent functions involving the generalized Srivastava-Attiya operator
On certain multivalent functions involving the generalized Srivastava-Attiya operator
en
en
In this paper, we introduce certain new classes of multivalent functions involving the generalized
Srivastava-Attiya operator. Such results as inclusion relationships, integral representation and arc length
problems for these classes of functions are obtained. The behavior of these classes under a certain integral
operator is also discussed.
6067
6076
Zhi-Gang
Wang
School of Mathematics and Computing Science
Hunan First Normal University
P. R. China
wangmath@163.com
Mohsan
Raza
Department of Mathematics
Government College University
Pakistan
mohsan976@yahoo.com
Muhammad
Ayaz
Department of Mathematics
Abdul Wali Khan University
Pakistan
mayazmath@awkum.edu.pk
Muhammad
Arif
Department of Mathematics
Abdul Wali Khan University
Pakistan
marifmaths@awkum.edu.pk
Srivastava-Attiya operator
starlike function
subordination.
Article.14.pdf
[
[1]
J. W. Alexander, Functions which map the interior of the unit circle upon simple regions, Ann. Math., 17 (1915), 12-22
##[2]
M. K. Aouf, A. O. Mostafa, H. M. Zayed, Some characterizations of integral operators associated with certain classes of p-valent functions defined by the Srivastava-Saigo-Owa fractional differintegral operator, Complex Anal. Oper. Theory, 10 (2016), 1267-1275
##[3]
M. Arif, K. I. Noor, M. Raza, Hankel determinant problem of a subclass of analytic functions, J. Inequal. Appl., 2012 (2012), 1-7
##[4]
J. H. Choi, M. Saigo, H. M. Srivastava, Some inclusion properties of a certain family of integral operators, J. Math. Anal. Appl., 276 (2002), 432-445
##[5]
J. Dziok, Meromorphic functions with bounded boundary rotation, Acta Math. Sci. Ser. B Engl. Ed., 34 (2014), 466-472
##[6]
R. M. El-Ashwah, M. K. Aouf, Some properties of new integral operator, Acta Univ. Apulensis Math. Inform., 24 (2010), 51-61
##[7]
S. Hussain, M. Arif, S. N. Malik, Higher order close-to-convex functions associated with Attiya-Srivastava operator, Bull. Iranian Math. Soc., 40 (2014), 911-920
##[8]
W. Janowski, Some extremal problems for certain families of analytic functions, I, Ann. Polon. Math., 28 (1973), 297-326
##[9]
J.-L. Liu, Subordinations for certain multivalent analytic functions associated with the generalized Srivastava- Attiya operator, Integral Transforms Spec. Funct., 19 (2008), 893-901
##[10]
Z.-H. Liu, Z.-G. Wang, F.-H. Wen, Y. Sun, Some subclasses of analytic functions involving the generalized Srivastava-Attiya operator, Hacet. J. Math. Stat., 41 (2012), 421-434
##[11]
P. Maheshwari, On modified Srivastava-Gupta operators, Filomat, 29 (2015), 1173-1177
##[12]
S. S. Miller, P. T. Mocanu, Differential subordinations, Theory and applications, Monographs and Textbooks in Pure and Applied Mathematics, Marcel Dekker, Inc., New York (2000)
##[13]
K. I. Noor, Higher order close-to-convex functions, Math. Japon., 37 (1992), 1-8
##[14]
K. I. Noor, M. Arif, Mapping properties of an integral operator,, Appl. Math. Lett., 25 (2012), 1826-1829
##[15]
K. I. Noor, W. Ul-Haq, M. Arif, S. Mustafa, On bounded boundary and bounded radius rotations, J. Inequal. Appl., 2009 (2009), 1-12
##[16]
K. S. Padmanabhan, R. Parvatham, Properties of a class of functions with bounded boundary rotation, Ann. Polon. Math., 31 (1975/76), 311-323
##[17]
B. Pinchuk, Functions of bounded boundary rotation, Israel J. Math., 10 (1971), 6-16
##[18]
Y. Polatoğlu, M. Bolcal, A. Şen, E. Yavuz, A study on the generalization of Janowski functions in the unit disc, Acta Math. Acad. Paedagog. Nyházi. (N.S.), 22 (2006), 27-31
##[19]
D. Răducanu, H. M Srivastava, A new class of analytic functions defined by means of a convolution operator involving the Hurwitz-Lerch zeta function, Integral Transforms Spec. Funct., 18 (2007), 933-943
##[20]
S. Shams, S. R. Kulkarni, J. M. Jahangiri, Subordination properties of p-valent functions defined by integral operators, Int. J. Math. Math. Sci., 2006 (2006), 1-3
##[21]
H. M. Srivastava, A. A. Attiya, An integral operator associated with the Hurwitz-Lerch zeta function and differential subordination, Integral Transforms Spec. Funct., 18 (2007), 207-216
##[22]
Y. Sun, W.-P. Kuang, Z.-G. Wang, Properties for uniformly starlike and related functions under the Srivastava- Attiya operator, Appl. Math. Comput., 218 (2011), 3615-3623
##[23]
N. Ularu, Properties for an integral operator on the class of close-to-convex functions, Filomat, 29 (2015), 1291-1296
##[24]
Z.-G. Wang, Z.-H. Liu, Y. Sun, Some properties of the generalized Srivastava-Attiya operator, Integral Transforms Spec. Funct., 23 (2012), 223-236
##[25]
Q.-H. Xu, H.-G. Xiao, H. M. Srivastava, Some applications of differential subordination and the Dziok-Srivastava convolution operator, Appl. Math. Comput., 230 (2014), 496-508
##[26]
S.-M. Yuan, Z.-M. Liu, Some properties of two subclasses of k-fold symmetric functions associated with Srivastava- Attiya operator, Appl. Math. Comput., 218 (2011), 1136-1141
]
Istratescu-Suzuki-Ćirić-type fixed points results in the framework of \(G\)-metric spaces
Istratescu-Suzuki-Ćirić-type fixed points results in the framework of \(G\)-metric spaces
en
en
The aim of this paper is to present fixed point results of convex contraction, convex contraction of order
2, weakly Zamfirescu and Ćirić strong almost contraction mappings in the framework of G-metric spaces.
Some examples are presented to support the results proved herein. As an application, we derive Suzuki type
fixed point in G-metric spaces. Our results generalize and extend various results in the existing literature.
We also present some examples to illustrate our new theoretical results.
6077
6095
Mujahid
Abbas
Department of Mathematics
Department of Mathematics and Applied Mathematics
University of Management and Technology
University of Pretoria
Pakistan
South Africa
abbas.mujahid@gmail.com
Azhar
Hussain
Department of Mathematics
University of Sargodha
Pakistan
hafiziqbal30@yahoo.com
Branislav
Popović
Faculty of Science
University of Kragujevac
Serbia
bpopovic@kg.ac.rs
Stojan
Radenović
Faculty of Mechanical Engineering
University of Belgrade
Serbia
radens@beotel.rs
Coincidence point
convex contraction
convex contraction of order 2
Ćirić strong almost contraction.
Article.15.pdf
[
[1]
M. Abbas, S. H. Khan, T. Nazir, Common fixed points of R-weakly commuting maps in generalized metric spaces, Fixed Point Theory Appl., 2011 (2011), 1-11
##[2]
M. Abbas, A. R. Khan, T. Nazir, Coupled common fixed point results in two generalized metric spaces, Appl. Math. Comput., 217 (2011), 6328-6336
##[3]
M. Abbas, T. Nazir, S. Radenović, Some periodic point results in generalized metric spaces, Appl. Math. Comput., 217 (2010), 4094-4099
##[4]
M. Abbas, T. Nazir, S. Radenović, Common fixed point of generalized weakly contractive maps in partially ordered G-metric spaces, Appl. Math. Comput., 218 (2012), 9383-9395
##[5]
M. Abbas, B. E. Rhoades, Common fixed point results for noncommuting mappings without continuity in generalized metric spaces, Appl. Math. Comput., 215 (2009), 262-269
##[6]
R. P. Agarwal, Z. Kadelburg, S. Radenović, On coupled fixed point results in asymmetric G-metric spaces, J. Inequal. Appl., 2013 (2013), 1-12
##[7]
M. A. Alghamdi, S. H. Alnafei, S. Radenović, N. Shahzad, Fixed point theorems for convex contraction mappings on cone metric spaces, Math. Comput. Modelling, 54 (2011), 2020-2026
##[8]
M. A. Alghamdi, E. Karapınar, \(G-\beta-\psi\)-contractive type mappings in G-metric spaces, Fixed Point Theory Appl., 2013 (2013), 1-17
##[9]
H. Aydi, B. Damjanović, B. Samet, W. Shatanawi, Coupled fixed point theorems for nonlinear contractions in partially ordered G-metric spaces, Math. Comput. Modelling, 54 (2011), 2443-2450
##[10]
H. Aydi, M. Postolache, W. Shatanawi, Coupled fixed point results for (\(\psi,\phi\))-weakly contractive mappings in ordered G-metric spaces, Comput. Math. Appl., 63 (2012), 298-309
##[11]
H. Aydi, W. Shatanawi, C. Vetro, On generalized weak G-contraction mapping in G-metric spaces, Comput. Math. Appl., 62 (2011), 4222-4229
##[12]
Y. J. Cho, B. E. Rhoades, R. Saadati, B. Samet, W. Shatanawi, Nonlinear coupled fixed point theorems in ordered generalized metric spaces with integral type, Fixed Point Theory Appl., 2012 (2012), 1-14
##[13]
R. Chugh, T. Kadian, A. Rani, B. E. Rhoades, Property P in G-metric spaces, Fixed Point Theory Appl., 2012 (2012), 1-12
##[14]
N. Hussain, M. A. Kutbi, S. Khaleghizadeh, P. Salimi, Discussions on recent results for \(\alpha-\psi\)-contractive mappings, Abstr. Appl. Anal., 2014 (2014), 1-13
##[15]
V. I. Istrăţescu, Some fixed point theorems for convex contraction mappings and mappings with convex diminishing diameters, I, Ann. Mat. Pura Appl., 130 (1982), 89-104
##[16]
M. Jleli, B. Samet, Remarks on G-metric spaces and fixed point theorems, Fixed Point Theory Appl., 2012 (2012), 1-7
##[17]
A. M. Miandaragh, M. Postolache, S. Rezapour, Approximate fixed points of generalized convex contractions, Fixed Point Theory Appl., 2013 (2013), 1-8
##[18]
Z. Mustafa, Common fixed points of weakly compatible mappings in G-metric spaces, Appl. Math. Sci. (Ruse), 6 (2012), 4589-4600
##[19]
Z. Mustafa, F. Awawdeh, W. Shatanawi, Fixed point theorem for expansive mappings in G-metric spaces, Int. J. Contemp. Math. Sci., 5 (2010), 2463-2472
##[20]
Z. Mustafa, H. Aydi, E. Karapınar, On common fixed points in G-metric spaces using (E.A) property, Comput. Math. Appl., 64 (2012), 1944-1956
##[21]
Z. Mustafa, M. Khandagji, W. Shatanawi, Fixed point results on complete G-metric spaces, Studia Sci. Math. Hungar., 48 (2011), 304-319
##[22]
Z. Mustafa, H. Obiedat, F. Awawdeh, Some fixed point theorem for mapping on complete G-metric spaces, Fixed Point Theory Appl., 2008 (2008), 1-12
##[23]
Z. Mustafa, W. Shatanawi, M. Bataineh, Existence of fixed point results in G-metric space, Int. J. Math. Math. Sci., 2009 (2009), 1-10
##[24]
Z. Mustafa, B. Sims, Some remarks concerning D-metric spaces, International Conference on Fixed Point Theory and Applications, Yokohama Publ., 2004 (2004), 189-198
##[25]
Z. Mustafa, B. Sims, A new approach to generalized metric spaces, J. Nonlinear Convex Anal., 7 (2006), 289-297
##[26]
Z. Mustafa, B. Sims, Fixed point theorems for contractive mappings in complete G-metric spaces, Fixed Point Theory Appl., 2009 (2009), 1-10
##[27]
H. Obiedat, Z. Mustafa, Fixed point results on a nonsymmetric G-metric spaces, Jordan J. Math. Stat., 3 (2010), 65-79
##[28]
S. Radenović, Remarks on some recent coupled coincidence point results in symmetric G-metric spaces, J. Oper., 2013 (2013), 1-8
##[29]
S. Radenović, P. Salimi, C. Vetro, T. Došenović, Edelstein-Suzuki-type results for self-mappings in various abstract spaces with application to functional equations, Acta Math. Sci. Ser. B Engl. Ed., 36 (2016), 94-110
##[30]
R. Saadati, S. M. Vaezpour, P. Vetro, B. E. Rhoades, Fixed point theorems in generalized partially ordered G-metric spaces, Math. Comput. Modelling, 52 (2010), 797-801
##[31]
B. Samet, C. Vetro, P. Vetro, Fixed point theorems for \(\alpha\psi\)-contractive type mappings, Nonlinear Anal., 75 (2012), 2154-2165
##[32]
B. Samet, C. Vetro, F. Vetro, Remarks on G-metric spaces, Int. J. Anal., 2013 (2013), 1-6
##[33]
W. Shatanawi, Fixed point theory for contractive mappings satisfying \(\Phi\)-maps in G-metric spaces, Fixed Point Theory Appl., 2010 (2010), 1-9
##[34]
W. Shatanawi, Some fixed point theorems in ordered G-metric spaces and applications, Abstr. Appl. Anal., 2011 (2011), 1-11
##[35]
T. Van An, N. Van Dung, Z. Kadelburg, S. Radenović, Various generalizations of metric spaces and fixed point theorems, Rev. R. Acad. Cienc. Exactas Fs. Nat. Ser. A Math. RACSAM, 109 (2015), 175-198
]
Hermite-Hadamard type inequalities for logarithmically B-preinvex functions
Hermite-Hadamard type inequalities for logarithmically B-preinvex functions
en
en
In this paper, we introduce the notion of logarithmically B-preinvex functions and establish certain new
Hermite-Hadamard type inequalities for the functions whose derivatives in absolute value are logarithmically
B-preinvex. Our results generalize several known results for the classes of logarithmically preinvex functions.
Some estimates for the left and right hand side of the Hermite-Hadamard inequality are also obtained for a
new class of differentiable logarithmically \(\alpha\)-preinvex functions.
6096
6112
Fiza
Zafar
Centre for Advanced Studies in Pure and Applied Mathematics (CASPAM)
Bahauddin Zakariya University
Pakistan
fizazafar@gmail.com
Nawab
Hussain
Department of Mathematics
King Abdulaziz University
Saudi Arabia
nhusain@kau.edu.sa
Nusrat
Yasmin
Centre for Advanced Studies in Pure and Applied Mathematics (CASPAM)
Bahauddin Zakariya University
Pakistan
nusyasmin@yahoo.com
Hina
Mehboob
Centre for Advanced Studies in Pure and Applied Mathematics (CASPAM)
Bahauddin Zakariya University
Pakistan
hinamahboob6@gmail.com
Hermite-Hadamard inequality
logarithmically B-preinvex functions
convex functions.
Article.16.pdf
[
[1]
A. Barani, A. G. Ghazanfari, S. S. Dragomir, Hermite{Hadamard inequality for functions whose derivatives absolute values are preinvex, J. Inequal. Appl., 2012 (2012), 1-9
##[2]
A. Ben-Israel, B. Mond, What is invexity?, J. Austral. Math. Soc. Ser. B, 28 (1986), 1-9
##[3]
M. A. Hanson, B. Mond, Convex Transformable Programming Problems and Invexity, J. Inform. Optim. Sci., 8 (1987), 201-207
##[4]
S. R. Mohan, S. K. Neogy, On invex sets and preinvex functions, J. Math. Anal. Appl., 189 (1995), 901-908
##[5]
M. A. Noor, Variational-like inequalities, Optimization, 30 (1994), 323-330
##[6]
M. A. Noor,, On Hadamard integral inequalities involving two log-preinvex functions, JIPAM. J. Inequal. Pure Appl. Math., 8 (2007), 1-14
##[7]
M. A. Noor,, Hadamard integral inequalities for product of two preinvex function, Nonlinear Anal. Forum, 14 (2009), 167-173
##[8]
M. A. Noor, K. I. Noor, M. U. Awan, J. Li, On Hermite-Hadamard Inequalities for h-preinvex functions, Filomat, 28 (2014), 1463-1474
##[9]
M. A. Noor, K. I. Noor, M. U. Awan, F. Qi, Integral inequalities of Hermite-Hadamard type for logarithmically h-preinvex functions, Cogent Math., 2 (2015), 1-10
##[10]
M. Z. Sarikaya, N. Alp, H. Bozkurt, On Hermite-Hadamard type integral inequalities for preinvex and log-preinvex functions, Contemp. Anal. Appl. Math., 1 (2013), 237-252
##[11]
S. K. Suneja, C. Singh, C. R. Bector, Generalization of preinvex and B-vex functions, J. Optim. Theory Appl., 76 (1993), 577-587
##[12]
S. H.Wang, X. M. Liu, New Hermite-Hadamard Type Inequalities for n-Times Differentiable and s-Logarithmically Preinvex Functions, Abst. Appl. Anal., 2014 (2014), 1-11
##[13]
T. Weir, B. Mond, Preinvex functions in multiobjective optimization, J. Math. Anal. Appl., 136 (1988), 29-38
]
A unified framework for the two-sets split common fixed point problem in Hilbert spaces
A unified framework for the two-sets split common fixed point problem in Hilbert spaces
en
en
The two-sets split common fixed point problem of two uniformly Lipschitzian asymptotically pseudocontractive
operators is considered. A unified framework for the study of this class of problems and class
of operators is provided. An iterative algorithm is constructed and strong convergence analysis is given.
6113
6125
Yonghong
Yao
Department of Mathematics
Tianjin Polytechnic University
China
yaoyonghong@aliyun.com
Limin
Leng
Department of Mathematics
Tianjin Polytechnic University
China
lenglimin@aliyun.com
Mihai
Postolache
Department of Mathematics and Informatics
China Medical University
University "Politehnica" of Bucharest
Taiwan
Romania
mihai@mathem.pub.ro
Xiaoxue
Zheng
Department of Mathematics
Tianjin Polytechnic University
China
zhengxiaoxue1991@aliyun.com
Split common fixed point
asymptotically pseudocontractive operators
strong convergence
Hilbert spaces.
Article.17.pdf
[
[1]
L.-C. Ceng, Q. H. Ansari, J.-C. Yao, An extragradient method for solving split feasibility and fixed point problems, Comput. Math. Appl., 64 (2012), 633-642
##[2]
Y. Censor, A. Segal, The split common fixed point problem for directed operators, J. Convex Anal., 16 (2009), 587-600
##[3]
S. S. Chang, L. Wang, Y. K. Tang, L. Yang, The split common fixed point problem for total asymptotically strictly pseudocontractive mappings, J. Appl. Math., 2012 (2012), 1-13
##[4]
P. Cholamjiak, Y. Shehu, Iterative approximation for split common fixed point problem involving an asymptotically nonexpansive semigroup and a total asymptotically strict pseudocontraction, Fixed Point Theory Appl., 2014 (2014), 1-14
##[5]
Q.-L. Dong, Y.-H. Yao, S.-N. He, Weak convergence theorems of the modified relaxed projection algorithms for the split feasibility problem in Hilbert spaces, Optim. Lett., 8 (2014), 1031-1046
##[6]
Z.-H. He, W.-S. Du, On hybrid split problem and its nonlinear algorithms, Fixed Point Theory Appl., 2013 (2013), 1-20
##[7]
P. E. Maingé, Approximation methods for common fixed points of nonexpansive mappings in Hilbert spaces, J. Math. Anal. Appl., 325 (2007), 469-479
##[8]
A. Moudafi, The split common fixed-point problem for demicontractive mappings, Inverse Probloms, 26 (2010), 1-6
]
Generation of discrete integrable systems and some algebro-geometric properties of related discrete lattice equations
Generation of discrete integrable systems and some algebro-geometric properties of related discrete lattice equations
en
en
With the help of infinite-dimensional Lie algebras and the Tu scheme, we address a discrete integrable
hierarchy to reduce the generalized relativistic Toda lattice (GRTL) system containing the relativistic Toda
lattice equation and its generalized lattice equation. Meanwhile, the Riemann theta functions are utilized
to present its algebro-geometric solutions. Besides, a reduced spectral problem is given to find an integrable
discrete hierarchy obtained via R-matrix theory, which can be reduced to the Toda lattice equation and a
generalized Toda lattice (GTL) system. The Lax pair and the infinite conservation laws of the GTL system
are also derived. Finally, the Hamiltonian structure of the GTL system is generated by the Poisson tensor.
6126
6141
Yufeng
Zhang
College of Mathematics
China University of Mining and Technology
P. R. China
mathzhang@126.com;zyfxz@cumt.edu.cn
Xiao-Jun
Yang
School of Mechanics and Civil Engineering
State Key Laboratory for Geo-Mechanics and Deep Underground Engineering
China University of Mining and Technology
China University of Mining and Technology
P. R. China
P. R. China
Spectral problem
algebro-geometric solution
R-matrix
Hamiltonian structure.
Article.18.pdf
[
[1]
M. Blaszak, K. Marciniak, R-matrix approach to lattice integrable systems, J. Math. Phys., 35 (1994), 4661-4682
##[2]
M. Blaszak, A. Szum, Lie algebraic approach to the construction of (2 + 1)-dimensional lattice-field and field integrable Hamiltonian equations, J. Math. Phys., 42 (2001), 225-259
##[3]
M. Blaszak, A. Szum, A. Prykarpatsky, Central extension approach to integrable field and lattice-field systems in (2 + 1)-dimensions, Proceedings of the XXX Symposium on Mathematical Physics, Toruń, (1998), Rep. Math. Phys., 44 (1999), 37-44
##[4]
E.-G. Fan, Z.-H. Yang, A lattice hierarchy with a free function and its reductions to the Ablowitz-Ladik and Volterra hierarchies, Internat. J. Theoret. Phys., 48 (2009), 1-9
##[5]
X.-G. Geng, H. H. Dai, Quasi-periodic solutions for some 2+1-dimensional discrete models, Phys. A, 319 (2003), 270-294
##[6]
X.-G. Geng, H. H. Dai, C.-W. Cao, Algebro-geometric constructions of the discrete Ablowitz-Ladik flows and applications, J. Math. Phys., 44 (2003), 4573-7588
##[7]
Y. C. Hon, E. G. Fan, An algebro-geometric solution for a Hamiltonian system with application to dispersive long wave equation, J. Math. Phys., 46 (2005), 1-21
##[8]
W.-X. Ma, A discrete variational identity on semi-direct sums of Lie algebras, J. Phys. A, 40 (2007), 15055-15069
##[9]
W.-X. Ma, B. Fuchssteiner, Algebraic structure of discrete zero curvature equations and master symmetries of discrete evolution equations, J. Math. Phys., 40 (1990), 2400-2418
##[10]
A. Pickering, Z.-N. Zhu, New integrable lattice hierarchies, Phys. Lett. A, 349 (2006), 439-445
##[11]
A. Pickering, Z.-N. Zhu, Darboux-Bäcklund transformation and explicit solutions to a hybrid lattice of the relativistic Toda lattice and the modified Toda lattice, Phys. Lett. A, 378 (2014), 1510-1513
##[12]
Z.-J. Qiao, A hierarchy of nonlinear evolution equations and finite-dimensional involutive systems, J. Math. Phys., 35 (1994), 2971-2992
##[13]
Z.-J. Qiao, Generalized r-matrix structure and algebro-geometric solution for integrable system, Rev. Math. Phys., 13 (2001), 545-586
##[14]
Z.-J. Qiao, The Camassa-Holm hierarchy, N-dimensional integrable systems, and algebro-geometric solution on a symplectic submanifold, Comm. Math. Phys., 239 (2003), 309-341
##[15]
M. Toda, Theory of nonlinear lattices, Translated from the Japanese by the author, Springer Series in Solid-State Sciences, Springer-Verlag, Berlin-New York (1981)
##[16]
G. Z. Tu, A trace identity and its applications to the theory of discrete integrable systems, J. Phys. A, 23 (1990), 3903-3922
##[17]
Y.-F. Zhang, B.-L. Feng, W.-J. Rui, X.-Z. Zhang, Algebro-geometric solutions with characteristics of a nonlinear partial differential equation with three-potential functions, Commun. Theor. Phys. (Beijing), 64 (2015), 81-89
##[18]
Y.-F. Zhang, W.-J. Rui, A few continuous and discrete dynamical systems, Rep. Math. Phys., 78 (2016), 19-32
##[19]
R.-G. Zhou, The finite-band solution of the Jaulent-Miodek equation, J. Math. Phys., 38 (1997), 2535-2546
##[20]
R.-G. Zhou, Q.-Y. Jiang, A Darboux transformation and an exact solution for the relativistic Toda lattice equation, J. Phys. A, 38 (2005), 7735-7742
##[21]
Z.-N. Zhu, Discrete zero curvature representations and infinitely many conservation laws for several 2+1 dimensional lattice hierarchies, ArXiv, 2003 (2003), 1-18
##[22]
Z.-N. Zhu, H.-C. Huang, Integrable discretizations for Toda-type lattice soliton equations, J. Phys. A, 32 (1999), 4171-4182
]
Semi-prequasi-invex type multiobjective optimization and generalized fractional programming problems
Semi-prequasi-invex type multiobjective optimization and generalized fractional programming problems
en
en
In this paper, we mainly discuss some applications of semi-prequasi-invex type functions for multiobjective optimization and generalized nonlinear programming problems. Some optimality results for semi-
prequasi-invex type multiobjective optimization problem are given, then some optimality necessary conditions under directional derivative and saddle point theories in semi-prequasi-invex type nonlinear programming problem are derived. Moreover, some duality theorems for the generalized nonlinear fractional
programming problem with semi-prequasi-invexity are also obtained. Our results improve the corresponding
ones in the literature.
6142
6152
Zai-Yun
Peng
College of Mathematics and Statistics
Chongqing JiaoTong University
P. R. China
pengzaiyun@126.com
Ke-Ke
Li
School of Mathematical Sciences
Chongqing Normal University
P. R. China
likeke135@163.com
Jian-Ting
Zhou
College of Civil Engineering
Chongqing JiaoTong University
P. R. China
jt-zhou@163.com
Semi-prequasi-invex functions
multiobjective optimization problem
nonlinear programming problem
generalized nonlinear fractional programming.
Article.19.pdf
[
[1]
T. Antczak, New optimality conditions and duality results of G type in differentiable mathematical programming, Nonlinear Anal., 66 (2007), 1617-1632
##[2]
A. Ben-Israel, B. Mond, What is invexity?, J. Austral. Math. Soc. Ser. B, 28 (1986), 1-9
##[3]
H.-Z. Luo, H.-X. Wu, On the relationships between G-preinvex functions and semistrictly G-preinvex functions, J. Comput. Appl. Math., 222 (2008), 372-380
##[4]
H.-Z. Luo, H.-X. Wu, Y.-H. Zhu, Remarks on criteria of prequasi-invex functions, Appl. Math. J. Chinese Univ. Ser. B, 19 (2004), 335-341
##[5]
H.-Z. Luo, Z. K. Xu, On characterizations of prequasi-invex functions, J. Optim. Theory Appl., 120 (2004), 429-439
##[6]
D. H. Martin, The essence of invexity, J. Optim. Theory Appl., 47 (1985), 65-76
##[7]
T. Weir, B. Mond, Pre-invex functions in multiple objective optimization, J. Math. Anal. Appl., 136 (1988), 29-38
##[8]
Z. K. Xu, Duality in generalized nonlinear fractional programming, J. Math. Anal. Appl., 169 (1992), 1-9
##[9]
X.-M. Yang, Problems of semi-pteinvexity and multiobjective programming, (Chinese) J. Chongqing Normal Univ. Nat. Sci., 1 (1994), 1-5
##[10]
X.-M. Yang, A note on preinvexity, J. Ind. Manag. Optim., 10 (2014), 1319-1321
##[11]
X. Q. Yang, G. Y. Chen, A class of nonconvex functions and pre-variational inequalities, J. Math. Anal. Appl., 169 (1992), 359-373
##[12]
X.-M. Yang, D. Li, On properties of preinvex functions, J. Math. Anal. Appl., 256 (2001), 229-241
##[13]
X.-M. Yang, D. Li, Semistrictly preinvex functions, J. Math. Anal. Appl., 258 (2001), 287-308
##[14]
X.-M. Yang, X. Q. Yang, K. L. Teo, Characterizations and applications of prequasi-invex functions, J. Optim. Theory Appl., 110 (2001), 645-668
##[15]
Y.-X. Zhao, A type of generalized convexity and applications in optimization theory, (In Chinese) Master Degree Thesis. Jinhua: Zhejiang Normal University, China (2005)
##[16]
Y.-X. Zhao, X.-G. Meng, H. Qiao, S.-Y. Wang, L. Coladas Uria, Characterizations of semi-prequasi-invexity, J. Syst. Sci. Complex., 27 (2014), 1008-1026
]
Local fractional Fourier method for solving modified diffusion equations with local fractional derivative
Local fractional Fourier method for solving modified diffusion equations with local fractional derivative
en
en
In this manuscript, in order to solve the boundary and initial value problem of modified diffusion equation
with local fractional derivative, we present the local fractional Fourier series method. The method can easily
convert the partial fractional differential equation into the ordinary fractional equation system. And several
test examples are given to show the procedure and reliability of the proposed technique.
6153
6160
Yong-Ju
Yang
School of Mathematics and Statistics
Nanyang Normal University
P. R. China
tomjohn1007@126.com
Yan-Ni
Chang
School of Mathematics and Statistics
Nanyang Normal University
P. R. China
gone0505@eyou.com
Shun-Qin
Wang
School of Mathematics and Statistics
Nanyang Normal University
P. R. China
dhtwsq@126.com
Local fractional Fourier series
local fractional derivative
modified diffusion equation.
Article.20.pdf
[
[1]
H. Aydi, M. Abbas, C. Vetro, Partial Hausdorff metric and Nadler's fixed point theorem on partial metric spaces, Topology Appl., 159 (2012), 3224-3242
##[2]
C.-M. Chen, Numerical methods for solving a two-dimensional variable-order modified diffusion equation, Appl. Math. Comput., 225 (2013), 62-78
##[3]
N. Heymans, I. Podlubny, Physical interpretation of initial conditions for fractional differential equations with Riemann-Liouville fractional derivatives, Rheol. Acta, 45 (2006), 765-771
##[4]
J. Hristov, Heat-balance integral to fractional (half-time) heat diffusion sub-model, Thermal Sci., 14 (2010), 291-316
##[5]
H. Jafari, H. Tajadodi, He's variational iteration method for solving fractional Riccati differential equation, Int. J. Differ. Equ., 2010 (2010), 1-8
##[6]
A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and applications of fractional differential equations, North- Holland Mathematics Studies, Elsevier,, Amsterdam (2006)
##[7]
K. M. Owolabi, K. C. Patidar, Higher-order time-stepping methods for time-dependent reaction-diffusion equations arising in biology, Appl. Math. Comput., 240 (2014), 30-50
##[8]
A. D. Polyanin, A. I. Zhurov, Functional constraints method for constructing exact solutions to delay reaction- diffusion equations and more complex nonlinear equations, Commun. Nonlinear Sci. Numer. Simul., 19 (2014), 62-78
##[9]
S.-Q. Wang, Y.-J. Yang, H. K. Jassim, Local fractional function decomposition method for solving inhomogeneous wave equations with local fractional derivative, Abstr. Appl. Anal., 2014 (2014), 1-7
##[10]
A. M. Wazwaz, Partial Differential Equations: Methods and Applications, Balkema Publishers, The Netherlands (2002)
##[11]
X.-J. Yang, Local fractional functional analysis and its applications, Asian Academic Publisher, Hong Kong (2011)
##[12]
X.-J. Yang, Advanced local fractional calculus and its applications, World Science Publisher, New York (2012)
##[13]
Y.-J. Yang, L.-Q. Hua, Variational iteration transform method for fractional differential equations with local fractional derivative, Abstr. Appl. Anal., 2014 (2014), 1-9
##[14]
X.-J. Yang, H. M. Srivastava, An asymptotic perturbation solution for a linear oscillator of free damped vibrations in fractal medium described by local fractional derivatives, Commun. Nonlinear Sci. Numer. Simul., 29 (2015), 499-504
##[15]
X.-J. Yang, J. A. Tenreiro Machado, H. M. Srivastava, A new numerical technique for solving the local fractional diffusion equation: two-dimensional extended differential transform approac, Appl. Math. Comput., 274 (2016), 143-151
]
Strong convergence of a hybrid algorithm in a Banach space
Strong convergence of a hybrid algorithm in a Banach space
en
en
In this paper, we study a hybrid algorithm for finding a common solution of a finite family of equilibrium
problems which is also a common fixed point of a finite family of asymptotically quasi-\(\phi\)-nonexpansive
mappings in a strictly convex and uniformly smooth Banach space which also has the Kadec-Klee property.
6161
6169
Qing
Yuan
Department of Mathematics
Linyi University
China
zjyuanq@yeah.net
Sun Young
Cho
Center for General Educatin
China Medical University
Taiwan
ooly61@hotmail.com
Xiaolong
Qin
Institute of Fundamental and Frontier Sciences
Department of Mathematics
University of Electronic Science and Technology of China
King Abdulaziz University
China
Saudi Arabia
qxlxajh@163.com
Mean valued algorithm
hybrid algorithm
convergence
variational inequality
hybrid algorithm.
Article.21.pdf
[
[1]
R. P. Agarwal, Y. J. Cho, X.-L. Qin, Generalized projection algorithms for nonlinear operators, Numer. Funct. Anal. Optim., 28 (2007), 1197-1215
##[2]
Y. I. Alber, Metric and generalized projection operators in Banach spaces: properties and applications, Theory and applications of nonlinear operators of accretive and monotone type, Lecture Notes in Pure and Appl. Math., Dekker, New York (1996)
##[3]
I. K. Argyros, S. George, Extending the applicability of a new Newton-like method for nonlinear equations, Commun. Optim. Theory, 2016 (2016), 1-9
##[4]
B. A. Bin Dehaish, X.-L. Qin, A. Latif, H. O. Bakodah, Weak and strong convergence of algorithms for the sum of two accretive operators with applications, J. Nonlinear Convex Anal., 16 (2015), 1321-1336
##[5]
E. Blum, W. Oettli, From optimization and variational inequalities to equilibrium problems, Math. Student, 63 (1994), 123-145
##[6]
D. Butnariu, S. Reich, A. J. Zaslavski, Asymptotic behavior of relatively nonexpansive operators in Banach spaces, J. Appl. Anal., 7 (2001), 151-174
##[7]
S. Y. Cho, W.-L. Li, S. M. Kang, Convergence analysis of an iterative algorithm for monotone operators, J. Inequal. Appl., 2013 (2013), 1-14
##[8]
S. Y. Cho, X.-L. Qin, On the strong convergence of an iterative process for asymptotically strict pseudocontractions and equilibrium problems, Appl. Math. Comput., 235 (2014), 430-438
##[9]
X. P. Ding, J. C. Yao, New coincidence theorems in FC-spaces with applications, Nonlinear Funct. Anal. Appl., 13 (2008), 447-463
##[10]
A. Genel, J. Lindenstrauss, An example concerning fixed points, Israel J. Math., 22 (1975), 81-86
##[11]
M. A. Khan, N. Yannelis, Equilibrium theory in infinite dimensional spaces, Springer-Verlag, Berlin (1991)
##[12]
J. K. Kim, Strong convergence theorems by hybrid projection methods for equilibrium problems and fixed point problems of the asymptotically quasi-\(\phi\)-nonexpansive mappings, Fixed Point Theory Appl., 2011 (2011), 1-15
##[13]
J. K. Kim, D. R. Sahu, S. Anwar, Browder's type strong convergence theorem for S-nonexpansive mappings, Bull. Korean Math. Soc., 47 (2010), 503-511
##[14]
B. Liu, C. Zhang,, Strong convergence theorems for equilibrium problems and quasi-\(\phi\)-nonexpansive mappings, Nonlinear Funct. Anal. Appl., 16 (2011), 365-385
##[15]
X.-L. Qin, Y. J. Cho, S. M. Kang, Convergence theorems of common elements for equilibrium problems and fixed point problems in Banach spaces, J. Comput. Appl. Math., 225 (2009), 20-30
##[16]
X.-L. Qin, J.-C. Yao, Weak convergence of a Mann-like algorithm for nonexpansive and accretive operators, J. Inequal. Appl., 2016 (2016), 1-9
##[17]
R. T. Rockafellar, Characterization of the subdifferentials of convex functions, Pacific J. Math., 17 (1996), 497-510
##[18]
T. V. Su, Second-order optimality conditions for vector equilibrium problems, J. Nonlinear Funct. Appl., 2015 (2015), 1-31
##[19]
W. Takahashi, Nonlinear functional analysis, Fixed point theory and its applications, Yokohama Publishers, Yokohama (2000)
##[20]
W. Takahashi, K. Zembayashi, Strong and weak convergence theorems for equilibrium problems and relatively nonexpansive mappings in Banach spaces, Nonlinear Anal., 70 (2009), 45-57
##[21]
W.-X. Wang, J.-M. Song, Hybrid projection methods for a bifunction and relatively asymptotically nonexpansive mappings, Fixed Point Theory Appl, 2013 (2013), 1-10
##[22]
C.-J. Zhang, J.-L. Li, B.-Q. Liu, Strong convergence theorems for equilibrium problems and relatively nonexpansive mappings in Banach spaces, Comput. Math. Appl., 61 (2011), 262-276
##[23]
C.-J. Zhang, J.-L. Li, M. Sun, Existence of solutions for abstract economic equilibrium problems and algorithm, Comput. Math. Appl., 52 (2006), 1471-1482
]
Oscillation Criteria for Third-order Nonlinear Neutral Differential Equations with Distributed Deviating Arguments
Oscillation Criteria for Third-order Nonlinear Neutral Differential Equations with Distributed Deviating Arguments
en
en
The aim of this paper is to investigate the oscillation and asymptotic behavior of a class of third-
order nonlinear neutral differential equations with distributed deviating arguments. By means of Riccati
transformation technique and some inequalities, we establish several sufficient conditions which ensure that
every solution of the studied equation is either oscillatory or converges to zero. Two examples are provided
to illustrate the main results.
6170
6182
Cuimei
Jiang
Qingdao Technological University
P. R. China
jiangcuimei2004@163.com
Tongxing
Li
LinDa Institute of Shandong Provincial Key Laboratory of Network Based Intelligent Computing
School of Informatics
Linyi University
Linyi University
P. R. China
P. R. China
litongx2007@163.com
Oscillation
asymptotic behavior
third-order neutral differential equation
distributed deviating argument.
Article.22.pdf
[
[1]
R. P. Agarwal, M. Bohner, W.-T. Li, Nonoscillation and oscillation: theory for functional differential equations, Monographs and Textbooks in Pure and Applied Mathematics, Marcel Dekker, Inc., New York (2004)
##[2]
B. Baculíková, J. Džurina, On the asymptotic behavior of a class of third order nonlinear neutral differential equations, Cent. Eur. J. Math., 8 (2010), 1091-1103
##[3]
B. Baculíková, J. Džurina, Oscillation of third-order neutral differential equations, Math. Comput. Modelling, 52 (2010), 215-226
##[4]
B. Baculíková, J. Džurina, Oscillation theorems for second order neutral differential equations, Comput. Math. Appl., 61 (2011), 94-99
##[5]
B. Baculíková, J. Džurina, Oscillation theorems for second-order nonlinear neutral differential equations, Comput. Math. Appl., 62 (2011), 4472-4478
##[6]
T. Candan, Oscillation criteria and asymptotic properties of solutions of third-order nonlinear neutral differential equations, Math. Methods Appl. Sci., 38 (2015), 1379-1392
##[7]
R. D. Driver, A mixed neutral system, Nonlinear Anal., 8 (1984), 155-158
##[8]
S. Fišnarová, R. Mařík, Oscillation criteria for neutral second-order half-linear differential equations with applications to Euler type equations, Bound. Value Probl., 2014 (2014), 1-14
##[9]
J. Hale, Theory of functional differential equations, Second edition, Applied Mathematical Sciences, Springer-Verlag, New York-Heidelberg (1977)
##[10]
Y. Jiang, T.-X. Li, Asymptotic behavior of a third-order nonlinear neutral delay differential equation, J. Inequal. Appl., 2014 (2014), 1-7
##[11]
G. S. Ladde, V. Lakshmikantham, B. G. Zhang, Oscillation theory of differential equations with deviating arguments, Monographs and Textbooks in Pure and Applied Mathematics, Marcel Dekker, Inc., New York (1987)
##[12]
T.-X. Li, B. Baculíková, J. Džurina, Oscillatory behavior of second-order nonlinear neutral differential equations with distributed deviating arguments, Bound. Value Probl., 2014 (2014), 1-15
##[13]
T.-X. Li, Yu. V. Rogovchenko, Asymptotic behavior of an odd-order delay differential equation, Bound. Value Probl., 2014 (2014), 1-10
##[14]
T.-X. Li, Yu. V. Rogovchenko, Asymptotic behavior of higher-order quasilinear neutral differential equations, Abstr. Appl. Anal., 2014 (2014), 1-11
##[15]
T.-X. Li, Yu. V. Rogovchenko, Oscillation of second-order neutral differential equations, Math. Nachr., 288 (2015), 1150-1162
##[16]
T.-X. Li, Yu. V. Rogovchenko, C.-H. Zhang, Oscillation of second-order neutral differential equations, Funkcial. Ekvac., 56 (2013), 111-120
##[17]
T.-X. Li, E. Thandapani, Oscillation of second-order quasi-linear neutral functional dynamic equations with distributed deviating arguments, J. Nonlinear Sci. Appl., 4 (2011), 180-192
##[18]
T.-X. Li, C.-H. Zhang, G.-J. Xing, Oscillation of third-order neutral delay differential equations, Abstr. Appl. Anal., 2012 (2012), 1-11
##[19]
M. T. Şenel, N. Utku, Oscillation criteria for third-order neutral dynamic equations with continuously distributed delay, Adv. Difference Equ., 2014 (2014), 1-15
##[20]
E. Thandapani, T.-X. Li, On the oscillation of third-order quasi-linear neutral functional differential equations, Arch. Math. (Brno), 47 (2011), 181-199
##[21]
A. Tiryaki, Oscillation criteria for a certain second-order nonlinear differential equations with deviating arguments, Electron. J. Qual. Theory Differ. Equ., 2009 (2009), 1-11
##[22]
P.-G. Wang, Oscillation criteria for second-order neutral equations with distributed deviating arguments, Comput. Math. Appl., 47 (2004), 1935-1946
##[23]
P.-G. Wang, H. Cai, Oscillatory criteria for higher order functional differential equations with damping, J. Funct. Spaces Appl., 2013 (2013), 1-5
##[24]
J. S. W. Wong, Necessary and sufficient conditions for oscillation of second order neutral differential equations, J. Math. Anal. Appl., 252 (2000), 342-352
##[25]
G.-J. Xing, T.-X. Li, C.-H. Zhang, Oscillation of higher-order quasi-linear neutral differential equations, Adv. Difference Equ., 2011 (2011), 1-10
##[26]
Q.-X. Zhang, L. Gao, Y.-H. Yu, Oscillation criteria for third-order neutral differential equations with continuously distributed delay, Appl. Math. Lett., 25 (2012), 1514-1519
]
Mild solutions of impulsive semilinear neutral evolution equations in Banach spaces
Mild solutions of impulsive semilinear neutral evolution equations in Banach spaces
en
en
This paper is concerned with the existence of mild solutions for impulsive semilinear neutral functional
integro-differential equations in Banach spaces. The existence result is obtained by using fractional power of
operators, Mönch fixed point theorem, the piecewise estimation method and semigroup theory. Applications
to partial differential systems are also given.
6183
6194
Xinan
Hao
School of Statistics
School of Mathematical Sciences
Qufu Normal University
Qufu Normal University
P. R. China
P. R. China
haoxinan2004@163.com
Lishan
Liu
School of Mathematical Sciences
Department of Mathematics and Statistics
Qufu Normal University
Curtin University
P. R. China
Australia
mathlls@163.com
Yonghong
Wu
Department of Mathematics and Statistics
Curtin University
Australia
yhwu@maths.curtin.edu.au
Semilinear neutral evolution equations
measure of non-compactness
mild solution
semigroup.
Article.23.pdf
[
[1]
N. Abada, M. Benchohra, H. Hammouche, Existence and controllability results for impulsive partial functional differential inclusions, Nonlinear Anal., 69 (2008), 2892-2909
##[2]
N. Abada, M. Benchohra, H. Hammouche, Existence and controllability results for nondensely defined impulsive semilinear functional differential inclusions, J. Differential Equations, 246 (2009), 3834-3863
##[3]
M. Benchohra, M. Guedda, M. Kirane, Impulsive semilinear functional differential equations, Nelīnīĭnī Koliv., 5 (2002), 297-305, translation in Nonlinear Oscil. (N. Y.), 5 (2002), 287-296
##[4]
M. Benchohra, J. Henderson, S. K. Ntouyas, Existence results for impulsive multivalued semilinear neutral functional differential inclusions in Banach spaces, J. Math. Anal. Appl., 263 (2001), 763-780
##[5]
M. Benchohra, J. Henderson, S. K. Ntouyas, Existence results for impulsive semilinear neutral functional differential equations in Banach spaces, Mem. Differential Equations Math. Phys., 25 (2002), 105-120
##[6]
M. Benchohra, J. Henderson, S. K. Ntouyas, Semilinear impulsive neutral functional differential inclusions in Banach spaces, Appl. Anal., 81 (2002), 951-963
##[7]
M. Benchohra, J. Henderson, S. K. Ntouyas, Impulsive differential equations and inclusions, Contemporary Mathematics and Its Applications,, Hindawi Publishing Corporation, New York (2006)
##[8]
T. Cardinali, P. Rubbioni, Impulsive mild solutions for semilinear differential inclusions with nonlocal conditions in Banach spaces, Nonlinear Anal., 75 (2012), 871-879
##[9]
Y.-K. Chang, J. J. Nieto, W.-S. Li, On impulsive hyperbolic differential inclusions with nonlocal initial conditions, J. Optim. Theory Appl., 140 (2009), 431-442
##[10]
P.-Y. Chen, Y.-X. Li, , Nonlinear Anal., 74 (2011), 3578-3588. , Mixed monotone iterative technique for a class of semilinear impulsive evolution equations in Banach spaces, Nonlinear Anal., 74 (2011), 3578-3588
##[11]
P.-Y. Chen, Y.-X. Li, H. Yang, Perturbation method for nonlocal impulsive evolution equations, Nonlinear Anal. Hybrid Syst., 8 (2013), 22-30
##[12]
J. P. Dauer, N. I. Mahmudov, Integral inequalities and mild solutions of semilinear neutral evolution equations, J. Math. Anal. Appl., 300 (2004), 189-202
##[13]
K. Deimling, Nonlinear functional analysis, Springer-Verlag, Berlin (1985)
##[14]
Z.-B. Fan, G. Li, Existence results for semilinear differential equations with nonlocal and impulsive conditions, J. Funct. Anal., 258 (2010), 1709-1727
##[15]
D. J. Guo, V. Lakshmikantham, Nonlinear problems in abstract cones, Notes and Reports in Mathematics in Science and Engineering, Academic Press, Boston (1988)
##[16]
W. M. Haddad, V. S. Chellabonia, S. G. Nersesov, Impulsive and hybrid dynamical systems: Stability, dissipativity, and control, Princeton Univ. Press, Princeton, New Jersey (2006)
##[17]
X. Hao, L.-S. Liu, Y.-H. Wu, Positive solutions for second order impulsive differential equations with integral boundary conditions, Commun. Nonlinear Sci. Numer. Simul., 16 (2011), 101-111
##[18]
H.-P. Heinz, On the behaviour of measures of noncompactness with respect to differentiation and integration of vector-valued functions, Nonlinear Anal., 7 (1983), 1351-1374
##[19]
E. Hernández, D. O'Regan, On a new class of abstract impulsive differential equations, Proc. Amer. Math. Soc., 141 (2013), 1641-1649
##[20]
E. Hernández, M. Rabello, H. R. Henríquez, Existence of solutions for impulsive partial neutral functional differential equations, J. Math. Anal. Appl., 331 (2007), 1135-1158
##[21]
P. Kumar, D. N. Pandey, D. Bahuguna, Existence of piecewise continuous mild solutions for impulsive functional differential equations with iterated deviating arguments, Electron. J. Differential Equations, 2013 (2013), 1-15
##[22]
V. Lakshmikantham, D. D. Baĭnov, P. S. Simeonov, Theory of impulsive differential equations, Series in Modern Applied Mathematics, World Scientific Publishing Co., Inc., Teaneck, NJ (1989)
##[23]
J. Liang, J. H. Liu, T.-J. Xiao, Nonlocal impulsive problems for nonlinear differential equations in Banach spaces, Math. Comput. Modelling, 49 (2009), 798-804
##[24]
J. H. Liu, Nonlinear impulsive evolution equations, Dynam. Contin. Discrete Impuls. Systems, 6 (1999), 77-85
##[25]
T. Paul, A. Anguraj, Existence and uniqueness of nonlinear impulsive integro-differential equations, Discrete Contin. Dyn. Syst. Ser. B, 6 (2006), 1191-1198
##[26]
A. Pazy, Semigroups of linear operators and applications to partial differential equations, Applied Mathematical Sciences, Springer-Verlag, New York (1983)
##[27]
Y. Peng, X. Xiang, W. Wei, Second-order nonlinear impulsive integro-differential equations of mixed type with time-varying generating operators and optimal controls on Banach spaces, Comput. Math. Appl., 57 (2009), 42-53
##[28]
S.-L. Xie, Z.-L. Yang, , , 46 (2003), 445-452. , Solvability of nonlinear impulsive Volterra integral equations and integro-differential equa- tions in Banach spaces, (Chinese) Acta Math. Sinica (Chin. Ser.), 46 (2003), 445-452
]
Huge analysis of Hepatitis C model within the scope of fractional calculus
Huge analysis of Hepatitis C model within the scope of fractional calculus
en
en
A model of Hepatitis C is considered using the concept of derivative with fractional order. Using the
benefits associated to Caputo derivative with fractional order, we study the existence and uniqueness of
the system solutions with the help of fixed-point theorem. We derive special solutions using an iterative
method. To see the efficiency of the used method, we present in detail the stability analysis of this method
together with the uniqueness of the special solutions.
6195
6203
Badr Saad T.
Alkahtani
Department of mathematics, college of science
King Saud University
Saudi Arabia
balqahtani1@ksu.edu.sa
Abdon
Atangana
Institute for groundwater Studies, Faculty of Natural and Agricultural Sciences
University of the Free State
South Africa
AtanganaA@ufs.ac.za
Ilknur
Koca
Department of Mathematics, Faculty of Sciences
Mehmet Akif Ersoy University
Turkey
ikoca@mehmetakif.edu.tr
Hepatitis C model
special solution
fixed point theorem
iterative method.
Article.24.pdf
[
[1]
A. Alsaedi, D. Baleanu, S. Etemad, S. Rezapour, On coupled systems of time-fractional differential problems by using a new fractional derivative, J. Funct. Spaces, 2016 (2016), 1-8
##[2]
A. Atangana, B. S. T. Alkahtani, Analysis of the Keller-Segel model with a fractional derivative without singular kernel, Entropy, 17 (2015), 4439-4453
##[3]
D. A. Benson, S. W. Wheatcraft, M. M. Meerschaert, The fractionalorder governing equation of Lévy motion, Water Resour. Res., 36 (2000), 1413-1423
##[4]
M. Caputo, Linear models of dissipation whose Q is almost frequency independent, II, Reprinted from Geophys. J. R. Astr. Soc., 13 (1967), 529-539, Fract. Calc. Appl. Anal., 11 (2008), 4-14
##[5]
M. Caputo, M. Fabrizio, A new definition of fractional derivative without singular kernel, Progr. Fract. Differ. Appl., 1 (2015), 73-85
##[6]
M. S. F. Chong, M. Shahrill, L. Crossley, A. Madzvamuse, The stability analyses of the mathematical models of hepatitis C virus infection, Mod. Appl. Sci., 9 (2015), 250-271
##[7]
A. Cloot, J. F. Botha, A generalised groundwater flow equation using the concept of non-integer order derivatives, Water SA, 32 (2006), 1-7
##[8]
J. H. Cushman, T. R. Ginn, Fractional advectiondispersion equation: a classical mass balance with convolution- Fickian flux, Water Resour. Res., 36 (2000), 3763-3766
##[9]
I. Koca, N. Ozalp, Analysis of a fractional-order couple model with acceleration in feelings, Sci. World J., 2013 (2013), 1-6
##[10]
J. Losada, J. J. Nieto, Properties of a new fractional derivative without singular kernel, Progr. Fract. Differ. Appl., 1 (2015), 87-92
##[11]
A. U. Neumann, N. P. Lam, H. Dahari, D. R. Gretch, T. E. Wiley, T. J. Layden, A. S. Perelson, Hepatitis C viral dynamics in vivo and the antiviral efficacy of interferon-\(\alpha\) therapy, Science, 282 (1998), 103-107
##[12]
Z. M. Odibat, S. Momani, Application of variational iteration method to nonlinear differential equations of fractional order, Int. J. Nonlinear Sci. Numer. Simul., 7 (2006), 27-34
##[13]
I. Podlubny, Geometric and physical interpretation of fractional integration and fractional differentiation, Dedicated to the 60th anniversary of Prof. Francesco Mainardi, Fract. Calc. Appl. Anal., 5 (2002), 367-386
]
New fixed point theorem for \(\varphi\)-contractions in KM-fuzzy metric spaces
New fixed point theorem for \(\varphi\)-contractions in KM-fuzzy metric spaces
en
en
In this paper, by modifying the class of gauge functions \(\Phi_w\) and \(\Phi_{w^*}\) , a new fixed point theorem for
\(\varphi\)-contractions in KM-fuzzy metric spaces with a t-norm of H-type is established. We also give an example
to illustrate the validity of our main results.
6204
6209
Jiaming
Jin
Department of Mathematics
Nanchang University
P. R. China
jiamingjin123@163.com
Chuanxi
Zhu
Department of Mathematics
Nanchang University
P. R. China
chuanxizhu@126.com
Haochen
Wu
Department of Mathematics
Nanchang University
P. R. China
Fixed point
Menger probabilistic metric space
H-type
\(\varphi\)-contraction.
Article.25.pdf
[
[1]
D. W. Boyd, J. S. W. Wong, On nonlinear contractions, Proc. Amer. Math. Soc., 20 (1969), 458-464
##[2]
L. Ćirić, Solving the Banach fixed point principle for nonlinear contractions in probabilistic metric spaces, Non- linear Anal., 72 (2010), 2009-2018
##[3]
J.-X. Fang, On \(\varphi\)-contractions in probabilistic and fuzzy metric spaces, Fuzzy Sets Systems, 267 (2015), 86-99
##[4]
O. Hadžić, E. Pap, Fixed Point Theory in Probabilistic Metric Spaces, Kluwer Academic Publishers, Dordrecht (2001)
##[5]
H. C. Hua, M. J. Chen, S. H. Wang, New result on fixed point theorems for \(\varphi\)-contractions in Menger spaces, Fixed Point Theory and Appl., 2015 (2015), 1-9
##[6]
J. Jachymsjki, On probabilistic \(\varphi\)-contractions on Menger spaces, Nonlinear Anal., 73 (2010), 2199-2203
##[7]
I. Kramosil, J. Michálek, Fuzzy metric and statistical metric spaces, Kybernetika, 11 (1975), 336-344
##[8]
D. Mihet, A class of contractions in fuzzy metrics spaces, Fuzzy Sets Systems, 161 (2010), 1131-1137
##[9]
A. Roldán, J. Martínez-Moreno, C. Roldán, Tripled fixed point theorem in fuzzy metric spaces and applications, Fixed Point Theory and Appl., 2013 (2013), 1-13
]
A higher order frozen Jacobian iterative method for solving Hamilton-Jacobi equations
A higher order frozen Jacobian iterative method for solving Hamilton-Jacobi equations
en
en
It is well-known that the solution of Hamilton-Jacobi equation may have singularity i.e., the solution is
non-smooth or nearly non-smooth. We construct a frozen Jacobian multi-step iterative method for solving
Hamilton-Jacobi equation under the assumption that the solution is nearly singular. The frozen Jacobian
iterative methods are computationally very efficient because a single instance of the iterative method uses a
single inversion (in the scene of LU factorization) of the frozen Jacobian. The multi-step part enhances the
convergence order by solving lower and upper triangular systems. The convergence order of our proposed
iterative method is \(3(m - 1)\) for \(m \geq 3\). For attaining good numerical accuracy in the solution, we use
Chebyshev pseudo-spectral collocation method. Some Hamilton-Jacobi equations are solved, and numerically
obtained results show high accuracy.
6210
6227
Ebraheem O.
Alzahrani
Department of Mathematics, Faculty of Science
King Abdulaziz University
Saudi Arabia
Eman S.
Al-Aidarous
Department of Mathematics, Faculty of Science
King Abdulaziz University
Saudi Arabia
Arshad M. M.
Younas
Department of Mathematics, Faculty of Science
King Abdulaziz University
Saudi Arabia
Fayyaz
Ahmad
Dipartimento di Scienza e Alta Tecnologia
ment de Fisica i Enginyeria Nuclear
Universita dell'Insubria
Universitat Politecnica de Catalunya
UCERD Islamabad
Italy
Spain
Pakistan
fayyaz.ahmad@upc.edu
Shamshad
Ahmad
Heat and Mass Transfer Technological Center
Technical University of Catalonia
Spain
Shahid
Ahmad
Department of Mathematics
Government College University Lahore
Pakistan
Hamilton-Jacobi equations
frozen Jacobian iterative methods
systems of nonlinear equations
Chebyshev pseudo-spectral collocation method.
Article.26.pdf
[
[1]
R. Abgrall, Numerical discretization of the first-order Hamilton-Jacobi equation on triangular meshes, Comm. Pure Appl. Math., 49 (1996), 1339-1373
##[2]
F. Ahmad, E. Tohidi, J. A. Carrasco, A parameterized multi-step Newton method for solving systems of nonlinear equations, Numer. Algorithms, 71 (2016), 631-653
##[3]
F. Ahmad, E. Tohidi, M. Z. Ullah, J. A. Carrasco, Higher order multi-step Jarratt-like method for solving systems of nonlinear equations: application to PDEs and ODEs, Comput. Math. Appl., 70 (2015), 624-636
##[4]
E. S. Al-Aidarous, E. O. Alzahrani, H. Ishii, A. M. M. Younas, Asymptotic analysis for the eikonal equation with the dynamical boundary conditions, Math. Nachr., 287 (2014), 1563-1588
##[5]
E. S. Al-Aidarous, E. O. Alzahrani, H. Ishii, A. M. M. Younas, A convergence result for the ergodic problem for Hamilton-Jacobi equations with Neumann-type boundary conditions, Proc. Roy. Soc. Edinburgh Sect. A, 146 (2016), 225-242
##[6]
E. S. Alaidarous, M. Z. Ullah, F. Ahmad, A. S. Al-Fhaid, An efficient higher-order quasilinearization method for solving nonlinear BVPs, J. Appl. Math., 2013 (2013), 1-11
##[7]
A. H. Bhrawy, E. H. Doha, M. A. Abdelkawy, R. A. Van Gorder, Jacobi-Gauss-Lobatto collocation method for solving nonlinear reaction-diffusion equations subject to Dirichlet boundary conditions, Appl. Math. Model., 40 (2016), 1703-1716
##[8]
M. G. Crandall, H. Ishii, P.-L. Lions, User's guide to viscosity solutions of second order partial differential equations, Bull. Amer. Math. Soc. (N.S.), 27 (1992), 1-67
##[9]
M. G. Crandall, P.-L. Lions, Viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc., 277 (1983), 1-42
##[10]
M. Dehghan, F. Fakhar-Izadi, The spectral collocation method with three different bases for solving a nonlinear partial differential equation arising in modeling of nonlinear waves, Math. Comput. Modelling, 53 (2011), 1865-1877
##[11]
E. H. Doha, A. H. Bhrawy, M. A. Abdelkawy, R. A. Van Gorder, Jacobi-Gauss-Lobatto collocation method for the numerical solution of 1 + 1 nonlinear Schrödinger equations, J. Comput. Phys., 261 (2014), 244-255
##[12]
E. H. Doha, A. H. Bhrawy, S. S. Ezz-Eldien, Efficient Chebyshev spectral methods for solving multi-term fractional orders differential equations, Appl. Math. Model., 35 (2011), 5662-5672
##[13]
A. Harten, B. Engquist, S. Osher, S. R. Chakravarthy, Uniformly high order accurate essentially non-oscillatory schemes, III, J. Comput. Phys., 131 (1997), 3-47
##[14]
G.-S. Jiang, D.-P. Peng, Weighted ENO schemes for Hamilton-Jacobi equations, SIAM J. Sci. Comput., 21 (2000), 2126-2143
##[15]
G.-S. Jiang, C.-W. Shu, Efficient implementation of weighted ENO schemes, J. Comput. Phys., 126 (1996), 202-228
##[16]
P.-L. Lions, Generalized solutions of Hamilton-Jacobi equations, Research Notes in Mathematics, Pitman (Advanced Publishing Program), Boston, Mass.-London (1982)
##[17]
P.-L. Lions, P. E. Souganidis, Convergence of MUSCL and filtered schemes for scalar conservation laws and Hamilton-Jacobi equations, Numer. Math., 69 (1995), 441-470
##[18]
X.-D. Liu, S. Osher, T. Chan, Weighted essentially non-oscillatory schemes, J. Comput. Phys., 115 (1994), 200-212
##[19]
H. Montazeri, F. Soleymani, S. Shateyi, S. S. Motsa, On a new method for computing the numerical solution of systems of nonlinear equations, J. Appl. Math., 2012 (2012), 1-15
##[20]
J. M. Ortega, W. C. Rheinboldt, Iterative solution of nonlinear equations in several variables, Academic Press, New York (1970)
##[21]
S. Osher, J. A. Sethian, Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations, J. Comput. Phys., 79 (1988), 12-49
##[22]
S. Osher, C.-W. Shu, High-order essentially nonoscillatory schemes for Hamilton-Jacobi equations, SIAM J. Numer. Anal., 28 (1991), 907-922
##[23]
U. Qasim, Z. Ali, F. Ahmad, S. Serra-Capizzano, M. Z. Ullah, M. Asma, Constructing frozen Jacobian iterative methods for solving systems of nonlinear equations, associated with ODEs and PDEs using the homotopy method,Constructing frozen Jacobian iterative methods for solving systems of nonlinear equations, associated with ODEs and PDEs using the homotopy method,Constructing frozen Jacobian iterative methods for solving systems of nonlinear equations, associated with ODEs and PDEs using the homotopy method,Constructing frozen Jacobian iterative methods for solving systems of nonlinear equations, associated with ODEs and PDEs using the homotopy method,Constructing frozen Jacobian iterative methods for solving systems of nonlinear equations, associated with ODEs and PDEs using the homotopy method,Constructing frozen Jacobian iterative methods for solving systems of nonlinear equations, associated with ODEs and PDEs using the homotopy method, Algorithms (Basel), 9 (2016), 1-17
##[24]
S. Qasim, Z. Ali, F. Ahmad, S. Serra-Capizzano, M. Z. Ullah, A. Mahmood, Solving systems of nonlinear equations when the nonlinearity is expensive, Comput. Math. Appl., 71 (2016), 1464-1478
##[25]
J. Shen, T. Tang, L.-L. Wang, Spectral methods: algorithms, analysis and applications, Springer Series in Computational Mathematics, Springer, (2011)
##[26]
P. E. Souganidis, Approximation schemes for viscosity solutions of Hamilton-Jacobi equations, J. Differential Equations, 59 (1985), 1-43
##[27]
G. Szegö, Orthogonal Polynomials, American Mathematical Society Colloquium Publications, American Mathematical Society, New York (1939)
##[28]
J. F. Traub, Itersative methods for the solution of equations, Prentice-Hall, Englewood Cliffs (1964)
##[29]
E. Tohidi, S. Lotfi Noghabi, An efficient Legendre pseudospectral method for solving nonlinear quasi bang-bang optimal control problems, J. Appl. Math. Stat. Inform., 8 (2012), 73-85
##[30]
M. Z. Ullah, S. Serra-Capizzano, F. Ahmad, An efficient multi-step iterative method for computing the numerical solution of systems of nonlinear equations associated with ODEs, Appl. Math. Comput., 250 (2015), 249-259
##[31]
M. Z. Ullah, F. Soleymani, A. S. Al-Fhaid, Numerical solution of nonlinear systems by a general class of iterative methods with application to nonlinear PDEs, Numer. Algorithms, 67 (2014), 223-242
]
Stability and bifurcation analysis of a discrete predator-prey model with Holling type III functional response
Stability and bifurcation analysis of a discrete predator-prey model with Holling type III functional response
en
en
The paper studies the dynamical behaviors of a discrete predator-prey system with Holling type III
functional response. More precisely, we investigate the local stability of equilibriums,
flip bifurcation and
Neimark-Sacker bifurcation of the model by using the center manifold theorem and the bifurcation theory.
And analyze the dynamic characteristics of the system in two-dimensional parameter-spaces, one can observe
the ''cluster'' phenomenon. Numerical simulations not only illustrate our results, but also exhibit the complex
dynamical behaviors of the model. The results show that we can more clearly and directly observe the chaotic
phenomenon, period-adding and Neimark-Sacker bifurcation from two-dimensional parameter-spaces and the
optimal parameters matching interval can also be found easily.
6228
6243
Jiangang
Zhang
Department of Mathematics
Lanzhou Jiaotong University
China
zhangjg7715776@126.com
Tian
Deng
Department of Mathematics
Lanzhou Jiaotong University
China
dengtian1990@163.com
Yandong
Chu
Department of Mathematics
Lanzhou Jiaotong University
China
cyd@mail.lzjtu.cn
Shuang
Qin
Department of Mathematics
Lanzhou Jiaotong University
China
qinshuangok@126.com
Wenju
Du
School of Traffic and Transportation
Lanzhou Jiaotong University
China
duwenjuok@126.com
Hongwei
Luo
Department of Mathematics
Department of Information Engineering
Lanzhou Jiaotong University
Gansu forestry technological College
China
China
lhw1220@126.com
Predator-prey system
stability
flip bifurcation
Neimark-Sacker bifurcation
cluster
parameter-space.
Article.27.pdf
[
[1]
S. Banerjee, A. Tsygvintsev, Stability and bifurcations of equilibria in a delayed Kirschner-Panetta model, Appl. Math. Lett., 40 (2015), 65-71
##[2]
J. Carr, Applications of centre manifold theory, Applied Mathematical Sciences, Springer-Verlag, New York--Berlin (1981)
##[3]
B.-S. Chen, J.-J. Chen, Bifurcation and chaotic behavior of a discrete singular biological economic system, Appl. Math. Comput., 219 (2012), 2371-2386
##[4]
M. Danca, S. Codreanu, B. Bako, Detailed analysis of a nonlinear prey-predator model, J. Biol. Phys., 23 (1997), 11-20
##[5]
E. M. Elabbasy, A. A. Elabbasy, Y. Zhang, Bifurcation analysis and chaos in a discrete reduced Lorenz system, Appl. Math. Comput., 228 (2014), 184-194
##[6]
R. K. Ghaziani, W. Govaerts, C. Sonck, Resonance and bifurcation in a discrete-time predator-prey system with Holling functional response, Nonlinear Anal. Real World Appl., 13 (2012), 1451-1465
##[7]
A. Gkana, L. Zachilas, Incorporating prey refuge in a preypredator model with a Holling type I functional response: random dynamics and population outbreaks, J. Biol. Phys., 39 (2013), 587-606
##[8]
A. Gkana, L. Zachilas, Non-overlapping generation species: complex prey-predator interactions, Int. J. Nonlinear Sci. Numer. Simul., 16 (2015), 207-219
##[9]
J. Guckenheimer, P. Holmes, Nonlinear oscillations, dynamical systems, and bifurcations of vector fields, Applied Mathematical Sciences, Springer-Verlag, New York (1983)
##[10]
K. P. Hadeler, I. Gerstmann, The discrete Rosenzweig model, Math. Biosci., 98 (1990), 49-72
##[11]
Z. He, X. Lai, Bifurcation and chaotic behavior of a discrete-time predator-prey system,, Nonlinear Anal. Real World Appl., 12 (2011), 403-417
##[12]
D.-P. Hu, H.-J. Cao, Bifurcation and chaos in a discrete-time predator-prey system of Holling and Leslie type, Commun. Nonlinear Sci. Numer. Simul., 22 (2015), 702-715
##[13]
Z.-Y. Hu, Z.-D. Teng, L. Zhang, Stability and bifurcation analysis in a discrete SIR epidemic model, Math. Comput. Simulation, 97 (2014), 80-93
##[14]
D. Jana, Chaotic dynamics of a discrete predator-prey system with prey refuge, Appl. Math. Comput., 224 (2013), 848-865
##[15]
Z.-J. Jing, J.-P. Yang, Bifurcation and chaos in discrete-time predator-prey system, Chaos Solitons Fractals, 27 (2006), 259-277
##[16]
Y. A. Kuznetsov, Elements of applied bifurcation theory, Second edition, Applied Mathematical Sciences, Springer-Verlag, New York (1998)
##[17]
S.-Y. Li, Z.-L. Xiong, Bifurcation analysis of a predator-prey system with sex-structure and sexual favoritism, Adv. Difference Equ., 2013 (2013), 1-24
##[18]
X.-L. Liu, D.-M. Xiao, Complex dynamic behaviors of a discrete-time predator-prey system, Chaos Solitons Fractals, 32 (2007), 80-94
##[19]
O. P. Misra, P. Sinha, C. Singh, Stability and bifurcation analysis of a prey-predator model with age based predation, Appl. Math. Model., 37 (2013), 6519-6529
##[20]
S. L. Qiu, C. Q. Wu, J. B. Chen, Qualitative analysis for a predator-prey model of Holling II-function response with nonlinear density dependence, Nat. Sci. ED, 34 (2006), 14-18
##[21]
C. Robinson, Dynamical systems, Stability, symbolic dynamics, and chaos, Studies in Advanced Mathematics, CRC Press, Boca Raton (1995)
##[22]
C. Robinson, Dynamical systems, Stability, symbolic dynamics, and chaos, Second edition, Studies in Advanced Mathematics, CRC Press, Boca Raton (1999)
##[23]
P. Sangapate, New sufficient conditions for the asymptotic stability of discrete time-delay systems, Adv. Difference Equ., 2012 (2012), 1-8
##[24]
C. Wang, X.-Y. Li, Further investigations into the stability and bifurcation of a discrete predator-prey model, J. Math. Anal. Appl., 422 (2015), 920-939
##[25]
S. Wiggins, Introduction to applied nonlinear dynamical systems and chaos, Second edition, Texts in Applied Mathematics, Springer-Verlag, New York (2003)
##[26]
G.-D. Zhang, Y. Shen, B.-S. Chen, Bifurcation analysis in a discrete differential-algebraic predator-prey system, Appl. Math. Model., 38 (2014), 4835-4848
##[27]
G.-D. Zhang, Y. Shen, B.-S. Chen, Bifurcation analysis in a discrete differential-algebraic predator-prey system, Appl. Math. Model., 38 (2014), 4835-4848
]
A three step iterative algorithm for common solutions of quasi-variational inclusions and fixed point problems of pseudocontractions
A three step iterative algorithm for common solutions of quasi-variational inclusions and fixed point problems of pseudocontractions
en
en
In this paper, quasi-variational inclusions and fixed point problems of pseudocontractions are investigated
based on a three step iterative process. Some convergence theorems are established in framework of Hilbert
spaces. Several special cases are also discussed. The results presented in this paper extend and improve the
corresponding results announced by many other authors.
6244
6259
Hui-Ying
Hu
Department of Mathematics
Shanghai Normal University
China
huiying1117@hotmail.com
Jin-Zuo
Chen
Department of Mathematics
Shanghai Normal University
China
chanjanegeoger@163.com
Monotone operator
quasi-variational inclusion
strictly pseudocontractive mapping
convex optimization
Hilbert space.
Article.28.pdf
[
[1]
R. P. Agarwal, Y. J. Cho, N. Petrot, Systems of general nonlinear set-valued mixed variational inequalities problems in Hilbert spaces, Fixed Point Theory and Appl., 2011 (2011), 1-10
##[2]
F. E. Browder, W. V. Petryshyn, Construction of fixed points of nonlinear mappings in Hilbert space, J. Math. Anal. Appl., 20 (1967), 197-228
##[3]
S.-S. Chang, Set-valued variational inclusions in Banach spaces, J. Math. Anal. Appl., 248 (2000), 438-454
##[4]
S.-S. Chang, Existence and approximation of solutions for set-valued variational inclusions in Banach space, Proceedings of the Third World Congress of Nonlinear Analysts, Part 1, Catania, (2000), Nonlinear Anal., 47 (2001), 538-594
##[5]
Y. J. Cho, X.-L. Qin, M.-J. Shang, Y.-F. Su, Generalized nonlinear variational inclusions involving (\(A,\eta\))- monotone mappings in Hilbert spaces, Fixed Point Theory and Appl., 2007 (2007), 1-6
##[6]
P. Cholamjiak, Y. J. Cho, S. Suantai, Composite iterative schemes for maximal monotone operators in reflexive Banach spaces, Fixed Point Theory and Appl., 2011 (2011), 1-10
##[7]
P. L. Combettes, V. R. Wajs, Signal recovery by proximal forward-backward splitting, Multiscale Model. Simul., 4 (2005), 1168-1200
##[8]
V. F. Dem'yanov, G. E. Stavroulakis, L. N. Polyakova, P. D. Panagiotopoulos, Quasidifferentiability and nonsmooth modelling in mechanics, engineering and economics, Nonconvex Optimization and its Applications, Kluwer Academic Publishers, Dordrecht (1996)
##[9]
K. Geobel, W. A. Kirk, Topics in metric fixed point theory, Cambridge Studies in Advanced Mathematics, Cambridge University Press, Cambridge (1990)
##[10]
P. Hartman, G. Stampacchia, On some non-linear elliptic differential-functional equations, Acta Math., 115 (1966), 271-310
##[11]
J. K. Kim, S. Y. Cho, X.-L. Qin, Some results on generalized equilibrium problems involving strictly pseudocontractive mappings, Acta Math. Sci. Ser. B Engl. Ed., 31 (2001), 2041-2057
##[12]
G. Marino, H.-K. Xu, A general iterative method for nonexpansive mappings in Hilbert spaces, J. Math. Anal. Appl., 318 (2006), 43-52
##[13]
X.-S. Meng, S. Y. Cho, X.-L. Qin, A general iterative algorithm for common solutions of quasi variational inclusion and fixed point problems, J. Nonlinear Sci. Appl., 9 (2016), 4137-4147
##[14]
M. A. Noor, Generalized set-valued variational inclusions and resolvent equations, J. Math. Anal. Appl., 228 (1998), 206-220
##[15]
M. A. Noor, K. I. Noor, Sensitivity analysis for quasi-variational inclusions, J. Math. Anal. Appl., 236 (1999), 290-299
##[16]
J.-W. Peng, Y. Wang, D. S. Shyu, J.-C. Yao, Common solutions of an iterative scheme for variational inclusions, equilibrium problems, and fixed point problems, J. Inequal. Appl., 2008 (2008), 1-15
##[17]
W. Takahashi, T. Tamura, Convergence theorems for a pair of nonexpansive mappings, J. Convex Anal., 5 (1998), 45-56
##[18]
I. Yamada, The hybrid steepest descent method for the variational inequality problem over the intersection of fixed point sets of nonexpansive mappings, Inherently parallel algorithms in feasibility and optimization and their applications, Haifa, (2000), 473-504, Stud. Comput. Math., North-Holland, Amsterdam (2001)
##[19]
Y.-H. Yao, Y.-C. Liou, S. M. Kang, Approach to common elements of variational inequality problems and fixed point problems via a relaxed extra gradient method, Comput. Math. Appl., 59 (2010), 3472-3480
##[20]
S.-S. Zhang, J. H. Lee, C. K. Chan, Algorithms of common solutions to quasi variational inclusion and fixed point problems, Appl. Math. Mech., 29 (2008), 571-581
]
Fixed point results for admissible mappings with application to integral equations
Fixed point results for admissible mappings with application to integral equations
en
en
This work is intended as an attempt to improve and simplify some recent fixed point theorems for (weak)
\(\alpha\)-admissible mappings and (\(\alpha,\beta\))-admissible mappings from several articles in the framework of \(b\)-metric
spaces. An application in proving the existence of solution for a class of nonlinear integral equations is given.
6260
6273
Huaping
Huang
School of Mathematical Sciences, Laboratory of Mathematics and Complex Systems, Ministry of Education
Beijing Normal University
China
mathhhp@163.com
Guantie
Deng
School of Mathematical Sciences, Laboratory of Mathematics and Complex Systems, Ministry of Education
Beijing Normal University
China
denggt@bnu.edu.cn
Stojan
Radenović
Faculty of Mechanical Engineering
University of Belgrade
Serbia
radens@beotel.net
Zhanmei
Chen
School of Mathematical Sciences, Laboratory of Mathematics and Complex Systems, Ministry of Education
Beijing Normal University
China
zhanmei9920106@sina.cn
\(\alpha\)-admissible mapping
fixed point
(\(\alpha،\beta\))-admissible mapping
\(b\)-continuous
integral equation.
Article.29.pdf
[
[1]
A. Aghajani, M. Abbas, J. R. Roshan, Common fixed point of generalized weak contractive mappings in partially ordered b-metric spaces, Math. Slovaca, 64 (2014), 941-960
##[2]
I. A. Bakhtin, The contraction mapping principle in almost metric space, (Russian) Functional analysis, Ulyanovsk. Gos. Ped. Inst., Ulyanovsk, 30 (1989), 26-37
##[3]
S. Banach, Sur les opérations dans les ensembles abstraits et leurs applications aux équations intégrales, Fund. Math., 3 (1922), 133-181
##[4]
S. Chandok, Some fixed point theorems for (\(\alpha,\beta\))-admissible Geraghty type contractive mappings and related results, Math. Sci. (Springer), 9 (2015), 127-135
##[5]
S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostraviensis, 1 (1993), 5-11
##[6]
H.-P. Huang, S. Radenović, J. Vujaković, On some recent coincidence and immediate consequences in partially ordered b-metric spaces, Fixed Point Theory and Appl., 2015 (2015), 1-18
##[7]
J. Jachymski, The contraction principle for mappings on a metric space with a graph, Proc. Amer. Math. Soc., 136 (2008), 1359-1373
##[8]
M. Jovanović, Z. Kadelburg, S. Radenović, Common fixed point results in metric-type spaces, Fixed Point Theory and Appl., 2010 (2010), 1-15
##[9]
W. A. Kirk, P. S. Srinivasan, P. Veeramani, Fixed points for mappings satisfying cyclical contractive conditions, Fixed Point Theory, 4 (2003), 79-89
##[10]
J. J. Nieto, R. Rodíguez-López, Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations, Acta Math. Sin. (Engl. Ser.), 23 (2007), 1-2205
##[11]
R. Pant, R. Panicker, Geraghty and Ćirić type fixed point theorems in b-metric spaces, J. Nonlinear Sci. Appl., 9 (2016), 5741-5755
##[12]
A. C. M. Ran, M. C. B. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc., 132 (2004), 1435-1443
##[13]
J. R. Roshan, V. Parvaneh, S. Sedghi, N. Shobkolaei, W. Shatanawi, Common fixed points of almost generalized \((\psi,\varphi)_s\)-contractive mappings in ordered b-metric spaces, Fixed Point Theory and Appl., 2013 (2013), 1-23
##[14]
P. Salimi, N. Hussain, S. Shukla, Sh. Fathollahi, S. Radenović, Fixed point results for cyclic \(\alpha-\psi\varphi\)-contractions with application to integral equations, J. Comput. Appl. Math., 290 (2015), 445-458
##[15]
B. Samet, C. Vetro, P. Vetro, Fixed point theorems for \(\alpha\psi\)-contractive type mappings, Nonlinear Anal., 75 (2012), 2154-2165
##[16]
S. Sedghi, N. Shobkolaei, J. R. Roshan, W. Shatanawi, Coupled fixed point theorems in Gb-metric spaces, Mat. Vesnik, 66 (2014), 190-201
##[17]
W. Shatanawi, Fixed and common fixed point for mapping satisfying some nonlinear contraction in b-metric spaces, J. Math. Anal., 7 (2016), 1-12
##[18]
W. Shatanawi, A. Pitea, R. Lazović, Contraction conditions using comparison functions on b-metric spaces, Fixed Point Theory and Appl., 2014 (2014), 1-11
##[19]
W. Sintunavarat, Fixed point results in b-metric spaces approach to the existence of a solution for nonlinear integral equations, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Math. RACSAM, 110 (2016), 585-600
##[20]
W. Sintunavarat, Nonlinear integral equations with new admissibility types in b-metric spaces, J. Fixed Point Theory Appl., 18 (2016), 397-416
]
A general composite steepest-descent method for hierarchical fixed point problems of strictly pseudocontractive mappings in Hilbert spaces
A general composite steepest-descent method for hierarchical fixed point problems of strictly pseudocontractive mappings in Hilbert spaces
en
en
In this paper, we propose general composite implicit and explicit steepest-descent schemes for hierarchical
fixed point problems of strictly pseudocontractive mappings in a real Hilbert space. These composite
steepest-descent schemes are based on the well-known viscosity approximation method, hybrid steepestdescent
method and strongly positive bounded linear operator approach. We obtain some strong convergence
theorems under suitable conditions. Our results supplement and develop the corresponding ones announced
by some authors recently in this area.
6274
6293
Lu-Chuan
Ceng
Department of Mathematics
Shanghai Normal University
China
zenglc@hotmail.com
Ching-Feng
Wen
Center for Fundamental Science, and Research Center for Nonlinear Analysis and Optimization
Kaohsiung Medical University
Taiwan
cfwen@kmu.edu.tw
General composite steepest-descent method
strictly pseudocontractive mapping
hierarchical fixed point problem
demiclosedness principle
nonexpansive mapping
fixed point.
Article.30.pdf
[
[1]
L.-C. Ceng, Q. H. Ansari, J.-C. Yao, Some iterative methods for finding fixed points and for solving constrained convex minimization problems, Nonlinear Anal., 74 (2011), 5286-5302
##[2]
L.-C. Ceng, S.-M. Guu, J.-C. Yao, A general composite iterative algorithm for nonexpansive mappings in Hilbert spaces, Comput. Math. Appl., 61 (2011), 2447-2455
##[3]
L.-C. Ceng, Z.-R. Kong, C.-F. Wen, On general systems of variational inequalities, Comput. Math. Appl., 66 (2013), 1514-1532
##[4]
L.-C. Ceng, A. Petruşel, S. Szentesi, J.-C. Yao, Approximation of common fixed points and variational solutions for one-parameter family of Lipschitz pseudocontractions, Fixed Point Theory, 11 (2010), 203-224
##[5]
R. Glowinski, Numerical methods for nonlinear variational problems, Springer Series in Computational Physics, Springer-Verlag, New York (1984)
##[6]
K. Goebel, W. A. Kirk, Topics in metric fixed point theory, Cambridge Studies in Advanced Mathematics, Cambridge University Press, Cambridge (1990)
##[7]
J. S. Jung, Strong convergence of iterative methods for k-strictly pseudo-contractive mappings in Hilbert spaces, Appl. Math. Comput., 215 (2010), 3746-3753
##[8]
J. S. Jung, A general composite iterative method for strictly pseudocontractive mappings in Hilbert spaces, Fixed Point Theory Appl., 2014 (2014), 1-21
##[9]
J.-L. Lions, Quelques méthodes de résolution des problémes aux limites non linéaires, (French) Dunod; Gauthier- Villars, Paris (1969)
##[10]
P.-E. Maingé, A. Moudafi, Strong convergence of an iterative method for hierarchical fixed-point problems, Pac. J. Optim., 3 (2007), 529-538
##[11]
G. Marino, H.-K. Xu, A general iterative method for nonexpansive mappings in Hilbert spaces, J. Math. Anal. Appl., 318 (2006), 43-52
##[12]
G. Marino, H.-K. Xu, Weak and strong convergence theorems for strict pseudo-contractions in Hilbert spaces, J. Math. Math. Appl., 329 (2007), 336-346
##[13]
C. H. Morales, J. S. Jung, Convergence of paths for pseudocontractive mappings in Banach spaces, Proc. Amer. Math. Soc., 128 (2000), 3411-3419
##[14]
A. Moudafi, Viscosity approximation methods for fixed-points problems, J. Math. Anal. Appl., 241 (2000), 46-55
##[15]
A. Moudafi, P.-E. Maingé, Towards viscosity approximations of hierarchical fixed-point problems, Fixed Point Theory Appl., 2006 (2006), 1-10
##[16]
J. T. Oden, Quantitative methods on nonlinear mechanics, Prentice-Hall, Englewood Cliffs, New Jersey (1986)
##[17]
N. Shioji, W. Takahashi, Strong convergence of approximated sequences for nonexpansive mappings in Banach spaces, Proc. Amer. Math. Soc., 125 (1997), 3641-3645
##[18]
W. Takahashi, Nonlinear functional analysis, Fixed point theory and its applications, Yokohama Publishers, Yokohama (2000)
##[19]
W. Takahashi, , , Yokohama, (2009). , Introduction to nonlinear and convex analysis, Yokohama Publishers, Yokohama (2009)
##[20]
M. Tian, A general iterative algorithm for nonexpansive mappings in Hilbert spaces, Nonlinear Anal., 73 (2010), 689-694
##[21]
M. Tian, A general iterative method based on the hybrid steepest descent scheme for nonexpansive mappings in Hilbert spaces, International Conference on Computational Intelligence and Software Engineering, 2010 (2010), 1-4
##[22]
H.-K. Xu, Iterative algorithms for nonlinear operators, J. London Math. Soc., 66 (2002), 240-256
##[23]
H.-K. Xu, Viscosity approximation methods for nonexpansive mappings, J. Math. Anal. Appl., 298 (2004), 279-291
##[24]
H.-K. Xu, T.-H. Kim, Convergence of hybrid steepest-descent methods for variational inequalities, J. Optim. Theory. Appl., 119 (2003), 185-201
##[25]
I. Yamada, The hybrid steepest-descent method for variational inequality problems over the intersection of the fixed-point sets of nonexpansive mappings, Inherently Parallel Algorithms in Feasibility and Optimization and Their Applications, edited by D. Butnariu, Y. Censor, S. Reich, North-Holland, Amsterdam, Holland, 2001 (2001), 473-504
##[26]
Y.-H. Yao, Y.-C. Liou, S. M. Kang, Approach to common elements of variational inequality problems and fixed point problems via a relaxed extragradient method, Comput. Math. Appl., 59 (2010), 3472-3480
##[27]
Y.-H. Yao, Y.-C. Liou, G. Marino, Two-step iterative algorithms for hierarchical fixed point problems and variational inequality problems, J. Appl. Math. Comput., 31 (2009), 433-445
##[28]
E. Zeidler, Nonlinear functional analysis and its applications, III, Variational methods and optimization, Translated from the German by L. F. Boron, Springer-Verlag, New York (1985)
]
On modified degenerate Changhee polynomials and numbers
On modified degenerate Changhee polynomials and numbers
en
en
The Changhee polynomials and numbers are introduced in [D. S. Kim, T. Kim, J.-J. Seo, Adv. Studies
Theor. Phys., 7 (2013), 993-1003], and some interesting identities and properties of these polynomials are
found by many researcher. In this paper, we consider the modified degenerate Changhee polynomials and
derive some new and interesting identities and properties of those polynomials.
6294
6301
Jongkyum
Kwon
Department of Mathematics Education and RINS
Gyeongsang National University
Republic of Korea
mathkjk26@hanmail.net
Jin-Woo
Park
Department of Mathematics Education
Daegu University
Republic of Korea
a0417001@knu.ac.kr
p-adic invariant integral on \(\mathbb{Z}_p\)
degenerate Changhee polynomials
modified degenerate Changhee polynomials.
Article.31.pdf
[
[1]
L. Comtet, Advanced combinatorics, The art of finite and infinite expansions, Revised and enlarged edition, D. Reidel Publishing Co., Dordrecht (1974)
##[2]
T. Kim, On a q-analogue of the p-adic log gamma functions and related integrals, J. Number Theory, 76 (1999), 320-329
##[3]
T. Kim, q-Volkenborn integration, Russ. J. Math. Phys., 9 (2002), 288-299
##[4]
T. Kim, Note on the Euler numbers and polynomials, Adv. Stud. Contemp. Math. (Kyungshang), 17 (2008), 131-136
##[5]
T. Kim, Some identities on the q-Euler polynomials of higher order and q-Stirling numbers by the fermionic p-adic integral on \(\mathbb{Z}_p\), Russ. J. Math. Phys., 16 (2009), 484-491
##[6]
T. Kim, Y. H. Kim, Generalized q-Euler numbers and polynomials of higher order and some theoretic identities, J. Inequal. Appl., 2010 (2010), 1-6
##[7]
T. Kim, D. S. Kim, A note on nonlinear Changhee differential equations, Russ. J. Math. Phys., 23 (2016), 88-92
##[8]
D. S. Kim, T. Kim, Generalized Boole numbers and polynomials, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Math. RACSAM, 110 (2016), 823-839
##[9]
D. S. Kim, T. Kim, On degenerate Bell numbers and polynomials, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Math. RACSAM, 2016 (2016), 1-12
##[10]
D. S. Kim, T. Kim, J.-J. Seo, A note on Changhee polynomials and numbers, Adv. Studies Theor. Phys., 7 (2013), 993-1003
##[11]
T. Kim, T. Mansour, S. H. Rim, J.-J. Seo, A note on q-Changhee polynomials and numbers, Adv. Studies Theor. Phys., 8 (2014), 35-41
##[12]
H.-I. Kwon, T. Kim, J.-J. Seo, A note on degenerate Changhee numbers and polynomials, Proc. Jangjeon Math. Soc., 18 (2015), 295-3056
##[13]
H.-I. Kwon, T. Kim, J.-J. Seo, Modified degenerate Euler polynomials, Adv. Stud. Contemp. Math. (Kyungshang), 26 (2016), 203-209
##[14]
J.-W. Park, On the twisted q-Changhee polynomials of higher order, J. Comput. Anal. Appl., 20 (2016), 424-431
##[15]
F. Qi, L.-C. Jang, H.-I. Kwon, Some new and explicit identities related with the Appell-type degenerate q-Changhee polynomials, Adv. Difference Equ., 2016 (2016), 1-8
##[16]
S.-H. Rim, J.-W. Park, S.-S. Pyo, J.-K. Kwon, The n-th twisted Changhee polynomials and numbers, Bull. Korean Math. Soc., 52 (2015), 741-749
##[17]
S. Roman, The umbral calculus, Pure and Applied Mathematics, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York (2005)
]
A regularity of split-biquaternionic-valued functions in Clifford analysis
A regularity of split-biquaternionic-valued functions in Clifford analysis
en
en
We examine corresponding Cauchy-Riemann equations by using the non-commutativity for the product
on split-biquaternions. Additionally, we describe the regularity of functions and properties of their differential equations on split-biquaternions. We investigate representations and calculations of the derivatives of
functions of split-biquaternionic variables.
6302
6311
Ji Eun
Kim
Department of Mathematics
Pusan National University
Republic of Korea
jeunkim@pusan.ac.kr
Kwang Ho
Shon
Department of Mathematics
Pusan National University
Republic of Korea
khshon@pusan.ac.kr
Cauchy-Riemann equations
regular function
split-quaternion
Clifford analysis.
Article.32.pdf
[
[1]
J. A. Emanuello, C. A. Nolder, Notions of Regularity for Functions of a Split-Quaternionic Variable, arXiv, 2015 (2015), 1-19
##[2]
J. Kajiwara, X. D. Li, K. H. Shon, Function spaces in complex and Clifford analysis, International conference on Finite or Infinite Dimensional Complex Analysis and its Applications, National Univ. Pub., Hanoi, Vietnam, Hue Univ., 14 (2006), 127-155
##[3]
J. E. Kim, The corresponding inverse of functions of multidual complex variables in Clifford analysis, J. Nonlinear Sci. Appl., 9 (2016), 4520-4528
##[4]
J. E. Kim, S. J. Lim, K. H. Shon, Regularity of functions on the reduced quaternion field in Clifford analysis, Abstr. Appl. Anal., 2014 (2014), 1-8
##[5]
J. E. Kim, K. H. Shon, The Regularity of functions on Dual split quaternions in Clifford analysis, Abstr. Appl. Anal., 2014 (2014), 1-8
##[6]
J. E. Kim, K. H. Shon, Polar coordinate expression of hyperholomorphic functions on split quaternions in Clifford analysis, Adv. Appl. Clifford Alg., 25 (2015), 915-924
##[7]
J. E. Kim, K. H. Shon, Inverse mapping theory on split quaternions in Clifford analysis, Filomat, 30 (2016), 1883-1890
##[8]
J. E. Kim, K. H. Shon, Properties of regular functions with values in bicomplex numbers, Bull. Korean Math. Soc., 53 (2016), 507-518
##[9]
M. Libine, An Invitation to Split Quaternionic Analysis, Hypercomplex Analysis and Applications, Springer, Basel (2011)
##[10]
N. Masrouri, Y. Yayli, M. H. Faroughi, M. Mirshafizadeh, Comments on differentiable over function of split quaternions, Revista Notas de Matemática, 7 (2011), 128-134
##[11]
K. Nono, Hyperholomorphic functions of a quaternion variable, Bull. Fukuoka Univ. Ed., 32 (1983), 21-37
##[12]
A. Sudbery, Quaternionic Analysis, Math. Proc. Cambridge Philos. Soc., 85 (1979), 199-224
]
Generalized hybrid algorithms for fixed point and mixed equilibrium problems in Banach spaces
Generalized hybrid algorithms for fixed point and mixed equilibrium problems in Banach spaces
en
en
The purpose of this paper is to introduce and investigate a more generalized hybrid shrinking projection
algorithm for finding a common solution for a system of generalized mixed equilibrium problems. A accelerated strong convergence theorem of common solutions is established in the framework of a non-uniformly
convex Banach space. These new results improve and extend the previously known ones in the literature.
6312
6332
Yinglin
Luo
Department of Mathematics
Tianjin Polytechnic University
China
tjluoyinglin@sina.com
Yongfu
Su
Department of Mathematics
Tianjin Polytechnic University
China
tjsuyongfu@163.com
Wenbiao
Gao
Department of Mathematics
Tianjin Polytechnic University
China
15822752271@163.com
Hybrid projection algorithm
monotone mapping
equilibrium problem
variational inequality
quasi-nonexpansive mapping
fixed point.
Article.33.pdf
[
[1]
Y. I. Alber, Metric and generalized projection operators in Banach spaces: properties and applications, Theory and applications of nonlinear operators of accretive and monotone type, Lecture Notes in Pure and Appl. Math., Dekker, New York (1996)
##[2]
A. Barbagallo, Existence and regularity of solutions to nonlinear degenerate evolutionary variational inequalities with applications to dynamic network equilibrium problems, Appl. Math. Comput., 208 (2009), 1-13
##[3]
B. A. Bin Dehaish, X.-L. Qin, A. Latif, H. O. Bakodah, Weak and strong convergence of algorithms for the sum of two accretive operators with applications, J. Nonlinear Convex Anal., 16 (2015), 1321-1336
##[4]
E. Blum, W. Oettli, From optimization and variational inequalities to equilibrium problems, Math. Student, 63 (1994), 123-145
##[5]
D. Butnariu, S. Reich, A. J. Zaslavski, Asymptotic behavior of relatively nonexpansive operators in Banach spaces, J. Appl. Anal., 7 (2001), 151-174
##[6]
S. Y. Cho, X.-L. Qin, On the strong convergence of an iterative process for asymptotically strict pseudocontractions and equilibrium problems, Appl. Math. Comput., 235 (2014), 430-438
##[7]
Y. J. Cho, X.-L. Qin, J. I. Kang, Convergence theorems based on hybrid methods for generalized equilibrium problems and fixed point problems, Nonlinear Anal., 71 (2009), 4203-4214
##[8]
S. Y. Cho, X.-L. Qin, L. Wang, Strong convergence of a splitting algorithm for treating monotone operators, Fixed Point Theory Appl., 2014 (2014), 1-15
##[9]
I. Cioranescu, Geometry of Banach spaces, duality mappings and nonlinear problems, Mathematics and its Applications, Kluwer Academic Publishers, Dordrecht (1990)
##[10]
S. Dafermos, A. Nagurney, A network formulation of market equilibrium problems and variational inequalities, Oper. Res. Lett., 3 (1984), 247-250
##[11]
K. Fan, A minimax inequality and applications, Inequalities, III, Proc. Third Sympos., Univ. California, Los Angeles, Calif., dedicated to the memory of Theodore S. Motzkin, (1969), 103-113, Academic Press, New York (1972)
##[12]
J. Gwinner, F. Raciti, Random equilibrium problems on networks, Math. Comput. Modelling, 43 (2006), 880-891
##[13]
Y. Haugazeau, Sur les inequations variationnelles et la minimization de fonctionnelles convexes, Doctoral Thesis, University of Paris, France (1968)
##[14]
R.-H. He, Coincidence theorem and existence theorems of solutions for a system of Ky Fan type minimax inequalities in FC-spaces, Adv. Fixed Point Theory, 2 (2012), 47-57
##[15]
J. K. Kim, Strong convergence theorems by hybrid projection methods for equilibrium problems and fixed point problems of the asymptotically quasi-\(\phi\)-nonexpansive mappings, Fixed Point Theory Appl., 2011 (2011), 1-15
##[16]
B. Liu, C. Zhang, Strong convergence theorems for equilibrium problems and quasi-\(\phi\)-nonexpansive mappings, Nonlinear Funct. Anal. Appl., 16 (2011), 365-385
##[17]
X.-L. Qin, Y. J. Cho, S. M. Kang, Convergence theorems of common elements for equilibrium problems and fixed point problems in Banach spaces, J. Comput. Appl. Math., 225 (2009), 20-30
##[18]
X.-L. Qin, S. Y. Cho, S. M. Kang, Strong convergence of shrinking projection methods for quasi-\(\phi\)-nonexpansive mappings and equilibrium problems, J. Comput. Appl. Math., 234 (2010), 750-760
##[19]
T. V. Su, Second-order optimality conditions for vector equilibrium problems, J. Nonlinear Funct. Anal, 2015 (2015), 1-31
##[20]
W. Takahashi, Nonlinear functional analysis, Fixed point theory and its applications, Yokohama Publishers, Yokohama (2000)
##[21]
W. Takahashi, K. Zembayashi, Strong and weak convergence theorems for equilibrium problems and relatively nonexpansive mappings in Banach spaces, Nonlinear Anal., 70 (2009), 45-57
##[22]
Z. M. Wang, X. Zhang, Shrinking projection methods for systems of mixed variational inequalities of Browder type, systems of mixed equilibrium problems and fixed point problems, J. Nonlinear Funct. Anal., 2014 (2014), 1-25
##[23]
C.-Q. Wu, Wiener-Hope equations methods for generalized variational inequalities, J. Nonlinear Funct. Anal., 2013 (2013), 1-10
##[24]
L.-J. Zhang, H. Tong, An iterative method for nonexpansive semigroups, variational inclusions and generalized equilibrium problems, Adv. Fixed Point Theory, 4 (2014), 325-343
]
Existence results for mixed Hadamard and Riemann-Liouville fractional integro-differential inclusions
Existence results for mixed Hadamard and Riemann-Liouville fractional integro-differential inclusions
en
en
In this paper, we investigate a new class of mixed initial value problems of Hadamard and Riemann-
Liouville fractional integro-differential inclusions. The existence of solutions for convex valued (the upper
semicontinuous) case is established by means of Krasnoselskii's fixed point theorem for multivalued maps
and nonlinear alternative criterion, while the existence result for non-convex valued maps (the Lipschitz
case) relies on a fixed point theorem due to Covitz and Nadler. Illustrative examples are also included.
6333
6347
Bashir
Ahmad
Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science
King Abdulaziz University
Saudi Arabia
bashirahmad_qau@yahoo.com
Sotiris K.
Ntouyas
Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science
Department of Mathematics
King Abdulaziz University
University of Ioannina
Saudi Arabia
Greece
sntouyas@uoi.gr
Jessada
Tariboon
Nonlinear Dynamic Analysis Research Center, Department of Mathematics, Faculty of Applied Science
Centre of Excellence in Mathematics
King Mongkut's University of Technology North Bangkok
CHE
Thailand
Thailand
jessada.t@sci.kmutnb.ac.th
Fractional differential inclusions
Hadamard derivative
Riemann-Liouville derivative
fixed point theorem.
Article.34.pdf
[
[1]
M. P. Aghababa, Finite-time chaos control and synchronization of fractional-order nonautonomous chaotic (hyperchaotic) systems using fractional nonsingular terminal sliding mode technique, Nonlinear Dynam., 69 (2012), 247-261
##[2]
M. P. Aghababa, A novel terminal sliding mode controller for a class of non-autonomous fractional-order systems, Nonlinear Dynam., 73 (2013), 679-688
##[3]
B. Ahmad, A. Alsaedi, S. Z. Nazemi, S. Rezapour, Some existence theorems for fractional integro-differential equations and inclusions with initial and non-separated boundary conditions, Bound. Value Probl., 2014 (2014), 1-40
##[4]
B. Ahmad, S. K. Ntouyas, Existence of solutions for fractional differential inclusions with four-point nonlocal Riemann-Liouville type integral boundary conditions, Filomat, 27 (2013), 1027-1036
##[5]
B. Ahmad, S. K. Ntouyas, A. Alsaedi, New results for boundary value problems of Hadamard-type fractional differential inclusions and integral boundary conditions, Bound. Value Probl., 2013 (2013), 1-14
##[6]
B. Ahmad, S. K. Ntouyas, J. Tariboon, A study of mixed Hadamard and Riemann-Liouville fractional integro- differential inclusions via endpoint theory, Appl. Math. Lett, 52 (2016), 9-14
##[7]
S. Balochian, M. Nazari, Stability of particular class of fractional differential inclusion systems with input delay, Control Intell. Syst., 42 (2014), 279-283
##[8]
C. Bardaro, P. L. Butzer, I. Mantellini, The foundations of fractional calculus in the Mellin transform setting with applications, J. Fourier Anal. Appl., 21 (2015), 961-1017
##[9]
P. L. Butzer, A. A. Kilbas, J. J. Trujillo, Compositions of Hadamard-type fractional integration operators and the semigroup property, J. Math. Anal. Appl., 269 (2002), 387-400
##[10]
J. Cao, C. Ma, Z. Jiang, S. Liu, Nonlinear dynamic analysis of fractional order rub-impact rotor system, Commun. Nonlinear Sci. Numer. Simul., 16 (2011), 1443-1463
##[11]
C. Castaing, M. Valadier, Convex analysis and measurable multifunctions, Lecture Notes in Mathematics, Springer-Verlag, Berlin-New York (1977)
##[12]
L.-C. Ceng, C.-M. Chen, C.-T. Pang, On a finite family of variational inclusions with the constraints of generalized mixed equilibrium and fixed point problems, J. Inequal. Appl., 2014 (2014), 1-38
##[13]
H. Covitz, S. B. Nadler, Jr., Multivalued contraction mappings in generalized metric spaces, Israel J. Math., 8 (1970), 5-11
##[14]
M. F. Danca, Approach of a class of discontinuous dynamical systems of fractional order: existence of solutions, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 21 (2011), 3273-3276
##[15]
K. Deimling, Multivalued differential equations, de Gruyter Series in Nonlinear Analysis and Applications, Walter de Gruyter & Co., Berlin (1992)
##[16]
M. O. Efe, Fractional order systems in industrial automation-a survey, IEEE Trans. Ind. Inform., 7 (2011), 582-591
##[17]
M. A. Ezzat, Theory of fractional order in generalized thermoelectric MHD, Appl. Math. Model., 35 (2011), 4965-4978
##[18]
V. Gafiychuk, B. Datsko, V. Meleshko, Mathematical modeling of time fractional reaction-diffusion systems, J. Comput. Appl. Math., 220 (2008), 215-225
##[19]
Z. Gao, Active disturbance rejection control for nonlinear fractional-order systems, Internat. J. Robust Nonlinear Control, 26 (2016), 876-892
##[20]
J. R. Graef, J. Henderson, A. Ouahab, Fractional differential inclusions in the Almgren sense, Fract. Calc. Appl. Anal., 18 (2015), 673-686
##[21]
A. Granas, J. Dugundji, Fixed point theory, Springer Monographs in Mathematics, Springer-Verlag, New York (2003)
##[22]
J. Hadamard, Essai sur l'etude des fonctions, donnees par leur developpement de Taylor, J. Mat. Pure Appl. (Ser. 4), 8 (1892), 10-186
##[23]
S. H. Hosseinnia, R. Ghaderi, A. Ranjbar, M. Mahmoudian, S. Momani, Sliding mode synchronization of an uncertain fractional order chaotic system, Comput. Math. Appl., 59 (2010), 1637-1643
##[24]
S.-C. Hu, N. S. Papageorgiou, Handbook of multivalued analysis, Vol. I, Theory. Mathematics and its Applications, Kluwer Academic Publishers, Dordrecht (1997)
##[25]
A. A. Kilbas, Hadamard-type fractional calculus, J. Korean Math. Soc., 38 (2001), 1191-1204
##[26]
A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and applications of fractional differential equations, North- Holland Mathematics Studies, Elsevier Science B.V., Amsterdam (2006)
##[27]
M. Kisielewicz, Differential inclusions and optimal control, Mathematics and its Applications (East European Series), Kluwer Academic Publishers Group/PWN|Polish Scientific Publishers, Dordrecht/Warsaw (1991)
##[28]
M. Kisielewicz, Stochastic differential inclusions and applications, Springer Optimization and Its Applications, Springer, New York (2013)
##[29]
N. Laskin, Fractional market dynamics, Economic dynamics from the physics point of view, Bad Honnef, (2000), Phys. A, 287 (2000), 482-492
##[30]
A. Lasota, Z. Opial, An application of the Kakutani-Ky Fan theorem in the theory of ordinary differential equations, Bull. Acad. Polon. Sci. Sr. Sci. Math. Astronom. Phys., 13 (1965), 781-786
##[31]
Y. Luo, Y.-Q. Chen, Y.-G. Pi, Experimental study of fractional order proportional derivative controller synthesis for fractional order systems, Mechatronics, 21 (2011), 204-214
##[32]
S. S. Majidabad, H. T. Shandiz, A. Hajizadeh, Nonlinear fractional-order power system stabilizer for multimachine power systems based on sliding mode technique, Internat. J. Robust Nonlinear Control, 25 (2015), 1548-1568
##[33]
S. K. Ntouyas, S. Etemad, J. Tariboon, Existence results for multi-term fractional differential inclusions, Adv. Difference Equ., 2015 (2015), 1-15
##[34]
N. Özdemir, D. Avcı, Optimal control of a linear time-invariant space-time fractional diffusion process, J. Vib. Control, 20 (2014), 370-380
##[35]
I. Petráš, R. L. Magin, Simulation of drug uptake in a two compartmental fractional model for a biological system, Commun. Nonlinear Sci. Numer. Simul., 16 (2011), 4588-4595
##[36]
A. Petrusel, Fixed points and selections for multi-valued operators, Semin. Fixed Point Theory Cluj-Napoca, 2 (2001), 3-22
##[37]
A. Pisano, M. R. Rapaić, Z. D. Jeličić, E. Usai, Sliding mode control approaches to the robust regulation of linear multivariable fractional-order dynamics, Internat. J. Robust Nonlinear Control, 20 (2010), 2045-2056
##[38]
J.-W. Sun, Q. Yin, Robust fault-tolerant full-order and reduced-order observer synchronization for differential inclusion chaotic systems with unknown disturbances and parameters, J. Vib. Control, 21 (2015), 2134-2148
##[39]
M. S. Tavazoei, M. Haeri, Synchronization of chaotic fractional-order systems via active sliding mode controller, Phys. A, 387 (2008), 57-70
##[40]
G. Toufik, Existence and controllability results for fractional stochastic semilinear differential inclusions, Differ. Equ. Dyn. Syst., 23 (2015), 225-240
##[41]
X. Wang, P. Schiavone, Harmonic three-phase circular inclusions in finite elasticity, Contin. Mech. Thermodyn., 27 (2015), 739-747
##[42]
C. Yin, S. Dadras, S.-M. Zhong, Y.-Q. Chen, Control of a novel class of fractional-order chaotic systems via adaptive sliding mode control approach, Appl. Math. Model., 37 (2013), 2469-2483
##[43]
X. Zhao, H.-T. Yang, Y.-Q. He, Identification of constitutive parameters for fractional viscoelasticity, Commun. Nonlinear Sci. Numer. Simul., 19 (2014), 311-322
]
A new modified semi-implicit midpoint rule for nonexpansive mappings and 2-generalized hybrid mappings
A new modified semi-implicit midpoint rule for nonexpansive mappings and 2-generalized hybrid mappings
en
en
In this paper, we present a new modified semi-implicit midpoint rule with the viscosity technique for
finding a common fixed point of nonexpansive mappings and 2-generalized hybrid mappings in a real Hilbert
space. The proposed algorithm is based on implicit midpoint rule and viscosity approximation method.
Under some mild conditions, the strong convergence of the iteration sequences generated by the proposed
algorithm is derived.
6348
6363
Yanlai
Song
College of Science
Zhongyuan University of Technology
China
songyanlai2009@163.com
Yonggang
Pei
Engineering Laboratory for Big Data Statistical Analysis and Optimal Control, College of Mathematics and Information Science
Henan Normal University
China
peiyg@163.com
Hilbert space
nonexpansive mapping
invex set
fixed point
semi-implicit midpoint rule.
Article.35.pdf
[
[1]
M. A. Alghamdi, M. A. Alghamdi, N. Shahzad, H.-K. Xu, The implicit midpoint rule for nonexpansive mappings, Fixed Point Theory Appl., 2014 (2014), 1-9
##[2]
W. Auzinger, R. Frank, Asymptotic error expansions for stiff equations: an analysis for the implicit midpoint and trapezoidal rules in the strongly stiff case, Numer. Math., 56 (1989), 469-499
##[3]
G. Bader, P. Deu hard, A semi-implicit mid-point rule for stiff systems of ordinary differential equations, Numer. Math., 41 (1983), 373-398
##[4]
C. Byrne, Iterative oblique projection onto convex sets and the split feasibility problem, Inverse Problems, 18 (2002), 441-453
##[5]
Y. Censor, T. Bortfeld, B. Martin, A. Trofimov, A unified approach for inversion problems in intensity-modulated radiation therapy, Phys. Med. Biol., 51 (2006), 2353-2365
##[6]
Y. Censor, T. Elfving, A multiprojection algorithm using Bregman projections in a product space, Numer. Algorithms, 8 (1994), 221-239
##[7]
Y. Censor, T. Elfving, N. Kopf, T. Bortfeld, The multiple-sets split feasibility problem and its applications for inverse problems, Inverse Problems, 21 (2005), 2071-2084
##[8]
Y. Censor, A. Motova, A. Segal, Perturbed projections and subgradient projections for the multiple-sets split feasibility problem, J. Math. Anal. Appl., 327 (2007), 1244-1256
##[9]
P. Deu hard, Recent progress in extrapolation methods for ordinary differential equations, SIAM Rev., 27 (1985), 505-535
##[10]
K. Goebel, W. A. Kirk, Topics in metric fixed point theory, Cambridge Studies in Advanced Mathematics, Cambridge University Press, Cambridge (1990)
##[11]
E. Hofer, A partially implicit method for large stiff systems of ODEs with only few equations introducing small time-constants, SIAM J. Numer. Anal., 13 (1976), 645-663
##[12]
M. Hojo, W. Takahashi, I. Termwuttipong, Strong convergence theorems for 2-generalized hybrid mappings in Hilbert spaces, Nonlinear Anal., 75 (2012), 2166-2176
##[13]
J. Hrabalová, P. Tomášek, On stability regions of the modified midpoint method for a linear delay differential equation, Adv. Difference Equ., 2013 (2013), 1-10
##[14]
A. E. Kastner-Maresch, The implicit midpoint rule applied to discontinuous differential equations, Computing, 49 (1992), 45-62
##[15]
P. Kocourek, W. Takahashi, J.-C. Yao, Fixed point theorems and weak convergence theorems for generalized hybrid mappings in Hilbert spaces, Taiwanese J. Math., 14 (2010), 2497-2511
##[16]
P. E. Maingé, Strong convergence of projected subgradient methods for nonsmooth and nonstrictly convex minimization, Set-Valued Anal., 16 (2008), 899-912
##[17]
G. Marino, H.-K. Xu, Weak and strong convergence theorems for strict pseudo-contractions in Hilbert spaces, J. Math. Anal. Appl., 329 (2007), 336-346
##[18]
E. Naraghirad, L.-J. Lin, Strong convergence theorems for generalized nonexpansive mappings on star-shaped set with applications, Fixed Point Theory Appl., 2014 (2014), 1-24
##[19]
X.-L. Qin, Y. J. Cho, J. I. Kang, S. M. Kang, Strong convergence theorems for an infinite family of nonexpansive mappings in Banach spaces, J. Comput. Anal. Appl., 230 (2009), 121-127
##[20]
C. Schneider, Analysis of the linearly implicit mid-point rule for differential-algebraic equations, Electron. Trans. Numer. Anal., 1 (1993), 1-10
##[21]
S. Somali, Implicit midpoint rule to the nonlinear degenerate boundary value problems, Int. J. Comput. Math., 79 (2002), 327-332
##[22]
S. Somali, S. Davulcu, Implicit midpoint rule and extrapolation to singularly perturbed boundary value problems, Int. J. Comput. Math.,, 75 (2000), 117-127
##[23]
H.-K. Xu, Iterative algorithms for nonlinear operators, J. London Math. Soc., 66 (2002), 240-256
##[24]
H.-K. Xu, Viscosity approximation methods for nonexpansive mappings, J. Math. Anal. Appl., 298 (2004), 279-291
##[25]
H.-K. Xu, , , 26 (2010), 17 pages., Iterative methods for the split feasibility problem in infinite-dimensional Hilbert spaces, Inverse Problems, 26 (2010), 1-17
##[26]
H.-K. Xu, M. A. Alghamdi, N. Shahzad, The viscosity technique for the implicit midpoint rule of nonexpansive mappings in Hilbert spaces, Fixed Point Theory Appl., 2015 (2015), 1-12
##[27]
Y.-H. Yao, Y. J. Cho, Y.-C. Liou, Algorithms of common solutions for variational inclusions, mixed equilibrium problems and fixed point problems, European J. Oper. Res., 212 (2011), 242-250
##[28]
Y.-H. Yao, M. A. Noor, On viscosity iterative methods for variational inequalities, J. Math. Anal. Appl., 325 (2007), 776-787
##[29]
Y.-H. Yao, N. Shahzad, Y.-C. Liou, Modified semi-implicit midpoint rule for nonexpansive mappings, Fixed Point Theory Appl., 2015 (2015), 1-15
##[30]
Z.-T. Yu, L.-J. Lin, C.-S. Chuang, Mathematical programming with multiple sets split monotone variational inclusion constraints, Fixed Point Theory Appl., 2014 (2014), 1-27
##[31]
Y.-L. Yu, C.-F. Wen, A modified iterative algorithm for nonexpansive mappings, J. Nonlinear Sci. Appl., 9 (2016), 3719-3726
##[32]
H. Zegeye, N. Shahzad, Convergence of Mann's type iteration method for generalized asymptotically nonexpansive mappings, Comput. Math. Appl., 62 (2011), 4007-4014
]
Integral inequalities of Simpsons type for (\(\alpha,m\))-convex functions
Integral inequalities of Simpsons type for (\(\alpha,m\))-convex functions
en
en
In this paper, we establish some integral inequalities of Simpson's type for (\(\alpha,m\))-convex functions.
6364
6370
Ye
Shuang
College of Mathematics
Inner Mongolia University for Nationalities
China
shuangye152300@sina.com
Yan
Wang
College of Mathematics
Inner Mongolia University for Nationalities
China
sella110@vip.qq.com
Feng
Qi
Department of Mathematics, College of Science
Institute of Mathematics
Tianjin Polytechnic University
Henan Polytechnic University
China
China
qifeng618@gmail.com;qifeng618@hotmail.com
Simpson's type integral inequality
(\(\alpha،m\))-convex function
application mean inequality.
Article.36.pdf
[
[1]
R.-F. Bai, F. Qi, B.-Y. Xi, Hermite-Hadamard type inequalities for the m- and (\(\alpha,m\))-logarithmically convex functions, Filomat, 27 (2013), 1-7
##[2]
S. S. Dragomir, On some new inequalities of Hermite-Hadamard type for m-convex functions, Tamkang J. Math., 33 (2002), 55-65
##[3]
S. S. Dragomir, R. P. Agarwal, Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula, Appl. Math. Lett., 11 (1998), 91-95
##[4]
S. S. Dragomir, G. Toader, Some inequalities for m-convex functions, Studia Univ. Babeş-Bolyai Math., 38 (1993), 21-28
##[5]
M. Klaričić Bakula, M. E. Özdemir, J. Pečarić, Hadamard type inequalities for m-convex and (\(\alpha,m\))-convex functions, J. Inequal. Pure Appl. Math., 9 (2008), 1-12
##[6]
V. G. Miheşan, A generalization of the convexity, Seminar on Functional Equations, Approx. Convex, Cluj-Napoca, Romania (1993)
##[7]
C. E. M. Pearce, J. Pečarić, Inequalities for differentiable mappings with application to special means and quadrature formula, Appl. Math. Lett., 13 (2000), 51-55
##[8]
F. Qi, B.-Y. Xi, Some Hermite-Hadamard type inequalities for geometrically quasi-convex functions, Proc. Indian Acad. Sci. Math. Sci., 124 (2014), 333-342
##[9]
F. Qi, T.-Y. Zhang, B.-Y. Xi, Hermite-Hadamard-type integral inequalities for functions whose first derivatives are convex, Ukrainian Math. J., 67 (2015), 625-640
##[10]
G. Toader, Some generalizations of the convexity, in: Proceedings of the Colloquium on Approximation and Optimization (Cluj-Napoca, 1985), Univ. Cluj-Napoca, Cluj, 1985 (1985), 329-338
##[11]
B.-Y. Xi, F. Qi, Hermite-Hadamard type inequalities for geometrically r-convex functions, Studia Sci. Math. Hungar., 51 (2014), 530-546
##[12]
B.-Y. Xi, F. Qi, Inequalities of Hermite-Hadamard type for extended s-convex functions and applications to means, J. Nonlinear Convex Anal., 16 (2015), 873-890
##[13]
B.-Y. Xi, T.-Y. Zhang, F. Qi, Some inequalities of Hermite-Hadamard type for m-harmonic-arithmetically convex functions, ScienceAsia, 41 (2015), 357-361
]
On the well-posedness of the incompressible flow in porous media
On the well-posedness of the incompressible flow in porous media
en
en
In this paper, we are concerned with the two-dimensional (2D) incompressible
flow in porous media
(IPM) in the whole space. We prove the local well-posedness of the solutions for the system in Besov spaces
of weak type and obtain blow-up criterion of solutions by particle trajectory method and Fourier localization
method.
6371
6381
Fuyi
Xu
School of Mathematics Science
School of Science
Qufu normal University
Shandong University of Technology
China
China
zbxufuyi@163.com
Lishan
Liu
School of Mathematics Science
Qufu normal University
China
mathlls@163.com
Well-posedness
blow-up criterion
particle trajectory mapping
Fourier localization method
Besov spaces of weak type.
Article.37.pdf
[
[1]
J. Beale, T. Kato, A. Majda, Remark on the breakdown of smooth solutions for the 3-D Euler equations, Comm. Math. Phys., 94 (1984), 61-66
##[2]
J. Bear, Dynamics of Fluids in Porous Media, Elsevier, New York (1972)
##[3]
J. Bergh, J. Löfstrom, Interpolation Spaces, An Introduction, Springer-Verlag, Berlin-New York (1976)
##[4]
D. Chae, On the well-posedness of the Euler equations in the Triebel-Lizorkin spaces, Comm. Pure Appl. Math., 55 (2002), 654-678
##[5]
D. Chae, On the Euler equations in the critical Triebel-Lizorkin spaces, Arch. Rational Mech. Anal., 170 (2003), 185-210
##[6]
D. Chae, Local existence and blow-up criterion for the Euler equations in the Besov spaces, Asymptot. Anal., 38 (2004), 339-358
##[7]
J.-Y. Chemin, Perfect incompressible fluids, Oxford Lectures Series in Mathematics and its Applications, The Clarendon Press, Oxford University Press, New York (1998)
##[8]
D. Córdoba, F. Gancedo, R. Orive, Analytical behavior of the two-dimensional incompressible flow in porous media, J. Math. Phys., 48 (2007), 1-19
##[9]
D. Nield, A. Bejan, Convection in Porous Media, Springer-Verlag, New York (1999)
##[10]
M. Price, Introducing Groundwater, 2nd ed., Chapman and Hall, London (1996)
##[11]
E. M. Stein, Harmonic Analysis, Princeton University Press, Princeton (1993)
##[12]
R. Takada, Local existence and blow-up criterion for the Euler equations in Besov spaces of weak type, J. Evol. Equ., 8 (2008), 693-725
##[13]
W. Yu, Y. He, On the well-posedness of the incompressible porous media equation in Triebel-Lizorkin spaces, Boundary Value Problems, 2014 (2014), 1-11
]
Characterizations of solution sets of set-valued generalized pseudoinvex optimization problems
Characterizations of solution sets of set-valued generalized pseudoinvex optimization problems
en
en
We study the Stampacchia equilibrium-like problems in terms of normal subdifferential for set-valued
maps and study their relations with set-valued optimization problems by the scalarization method.
Characterizations of the solution sets of generalized pseudoinvex extremum problems are established.
6382
6395
Lu-Chuan
Ceng
Department of Mathematics
Shanghai Normal University
China
zenglc@hotmail.com
Abdul
Latif
Department of Mathematics
King Abdulaziz University
Saudi Arabia
alatif@kau.edu.sa
Set-valued maps
normal subdifferential
solution set
Stampacchia equilibrium-like problem.
Article.38.pdf
[
[1]
M. Alshahrani, Q. H. Ansari, S. Al-Homidan, Nonsmooth variational-like inequalities and nonsmooth vector optimization, Optim. Lett., 8 (2014), 739-751
##[2]
Q. H. Ansari, M. Rezaei, Generalized pseudolinearity, Optim. Lett., 6 (2012), 241-251
##[3]
T. Q. Bao, B. S. Mordukhovich, Variational principles for set-valued mappings with applications to multiobjective optimization, Control Cybernet, 36 (2007), 531-562
##[4]
L.-C. Ceng, G.-Y. Chen, X.-X. Huang, J.-C. Yao, Existence theorems for generalized vector variational inequalities with pseudomonotonicity and their applications, Taiwanese J. Math., 12 (2008), 151-172
##[5]
L.-C. Ceng, S.-C. Huang, Existence theorems for generalized vector variational inequalities with a variable ordering relation, J. Global Optim., 46 (2010), 521-535
##[6]
L.-C. Ceng, A. Latif, Q. H. Ansari, Y.-C. Yao, Hybrid Extragradient Method for Hierarchical Variational Inequalities, Fixed Point Theory and Appl., 2014 (2014), 1-35
##[7]
L.-C. Ceng, A. Latif, J.-C. Yao, On solutions of a system of variational inequalities and fixed point problems in Banach spaces, Fixed Point Theory and Appl., 2013 (2013), 1-34
##[8]
L.-C. Ceng, B. S. Mordukhovich, J.-C. Yao, Hybrid approximate proximal method with auxiliary variational inequality for vector optimization, J. Optim. Theory Appl., 146 (2010), 267-303
##[9]
L.-C. Ceng, S. Schaible, J.-C. Yao, Existence of solutions for generalized vector variational-like inequalities, J. Optim. Theory Appl., 137 (2008), 121-133
##[10]
G.-Y. Chen, X.-X. Huang, X.-Q. Yang, Vector Optimization, Set-valued and variational analysis, Lecture Notes in Economics and Mathematical Systems, Springer-Verlag, Berlin (2005)
##[11]
F. Giannessi, Theorems of alternative, quadratic programs and complementarity problems, Variational inequalities and complementarity problems, Proc. Internat. School, Erice, (1978), 151-186, Wiley, Chichester (1980)
##[12]
X.-X. Huang, J.-C. Yao, Characterizations of the nonemptiness and compactness for solution sets of convex set-valued optimization problems, J. Global Optim., 55 (2013), 611-625
##[13]
V. Jeyakumar, X.-Q. Yang, On characterizing the solution sets of pseudolinear programs, J. Optim. Theory Appl., 87 (1995), 745-755
##[14]
A. Latif, L.-C. Ceng, S. A. Al-Mezel, Some Iterative Methods for Convergence with Hierarchical Optimization and Variational Inclusions, J. Nonlinear Convex Anal., 17 (2016), 735-755
##[15]
A. Latif, L.-C. Ceng, Q. H. Ansari, Multi-step hybrid viscosity method for systems of variational inequalities defined over sets of solutions of an equilibrium problem and fixed point problems, Fixed Point Theory and Appl., 2012 (2012), 1-26
##[16]
C.-P. Liu, X.-M. Yang, H.-W. Lee, Characterizations of the solution sets of pseudoinvex programs and variational inequalities, J. Inequal. Appl., 2011 (2011), 1-13
##[17]
O. L. Mangasarian, A simple characterization of solution sets of convex programs, Oper. Res. Lett., 7 (1988), 21-26
##[18]
S. K. Mishra, K. K. Lai, On characterization of solution sets of nonsmooth pseudoinvex minimization problems, International Joint Conference on Computational Sciences and Optimization (CSO), Los Alamitos, (2009), IEEE Comput. Soc., 2 (2009), 739-741
##[19]
S. R. Mohan, S. K. Neogy, On invex sets and preinvex functions, J. Math. Anal. Appl., 189 (1995), 901-908
##[20]
B. S. Mordukhovich, Maximum principle in the problem of time optimal response with nonsmooth constraints, (Russian), translated from Prikl. Mat. Meh., 40 (1976), 1014-1023, J. Appl. Math. Mech., 40 (1976), 960-969
##[21]
B. S. Mordukhovich, Variational analysis and generalized differentiation, Basic theory, Grundlehren der Math- ematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], Springer-Verlag, Berlin (2006)
##[22]
S. B. Nadler Jr., Multi-valued contraction mappings, Pacific J. Math., 30 (1969), 475-488
##[23]
M. Oveisiha, J. Zafarani, Super efficient solutions for set-valued maps, Optimization, 62 (2013), 817-834
##[24]
M. Oveisiha, J. Zafarani, On characterization of solution sets of set-valued pseudoinvex optimization problems, J. Optim. Theory Appl., 163 (2014), 387-398
##[25]
M. Rezaie, J. Zafarani, Vector optimization and variational-like inequalities, J. Global Optim., 43 (2009), 47-66
##[26]
L. B. Santos, M. Rojas-Medar, G. Ruiz-Garzón, A. Rufión-Lizana, Existence of weakly efficient solutions in nonsmooth vector optimization, Appl. Math. Comput., 200 (2008), 547-556
##[27]
X. M. Yang, On characterizing the solution sets of pseudoinvex extremum problems, J. Optim. Theory Appl., 140 (2009), 537-542
##[28]
L.-C. Zeng, J.-C. Yao, An existence result for generalized vector equilibrium problems without pseudomonotonicity, Appl. Math. Lett., 19 (2006), 1320-1326
##[29]
L.-C. Zeng, J.-C. Yao, Existence of solutions of generalized vector variational inequalities in reflexive Banach spaces, J. Global Optim., 36 (2006), 483-497
##[30]
L.-C. Zeng, J.-C. Yao, Generalized Minty's lemma for generalized vector equilibrium problems, Appl. Math. Lett., 20 (2007), 32-37
##[31]
K. Q. Zhao, X. Wan, X. M. Yang, A note on characterizing solution set of nonsmooth pseudoinvex optimization problem, Optim. Lett., 7 (2013), 117-126
##[32]
K. Q. Zhao, X. M. Yang, Characterizations of the solution set for a class of nonsmooth optimization problems, Optim. Lett., 7 (2013), 685-694
]
Fixed points of the multifunction concerning \(F\)-contractions in partial metric spaces
Fixed points of the multifunction concerning \(F\)-contractions in partial metric spaces
en
en
In this paper, we prove some new fixed point theorems for multi-valued mappings under new contractions by proposing a new class of functions. The results of this paper improve several results in the literatures. And we extend the results into metric-like spaces, which expand the application range of the results.
6396
6407
Qianwen
Yu
Department of Mathematics
Nanchang University
P. R. China
Chuanxi
Zhu
Department of Mathematics
Nanchang University
P. R. China
chuanxizhu@126.com
Zhaoqi
Wu
Department of Mathematics
Nanchang University
P. R. China
\(F\)-contraction
fixed point
multi-valued mappings
partial metric space.
Article.39.pdf
[
[1]
T. Abdeljawad, E. Karapınar, K. Taş, Existence and uniqueness of a common fixed point on partial metric spaces, Appl. Math. Lett., 24 (2011), 1900-1904
##[2]
S. M. A. Aleomraninejad, I. M. Erhan, M. A. Kutbi, M. Shokouhnia, Common fixed point of multifunctions on partial metric spaces, Fixed Point Theory and Appl., 2015 (2015), 1-11
##[3]
S. M. A. Alemoraninejad, S. Rezapour, N. Shahzad, On fixed point generalizations of Suzuki's method, Appl. Math. Lett., 24 (2011), 1037-1040
##[4]
I. Altun, H. Simsek, ome fixed point theorems on dualistic partial metric spaces, J. Adv. Math. Stud., 1 (2008), 1-8
##[5]
I. Altun, F. Sola, H. Simsek, Generalized contractions on partial metric spaces, Topology Appl., 157 (2010), 2778-2785
##[6]
H. Aydi, M. Abbas, C. Vetro, Partial Hausdorff metric and Nadler's fixed point theorem on partial metric spaces, Topology Appl., 159 (2012), 3234-3242
##[7]
B. S. Choudhury, P. Konar, B. E. Rhoades, N. Metiya, Fixed point theorems for generalized weakly contractive mappings, Nonlinear Anal., 74 (2011), 2116-2126
##[8]
S. Dhompongsa, H. Yingtaweesittikul, Fixed points for multivalued mappings and the metric completeness, Fixed Point Theory and Appl., 2009 (2009), 1-15
##[9]
X.-J. Huang, C.-X. Zhu, X. Wen, Fixed point theorems for expanding mappings in partial metric spaces, An. Ştiinţ. Univ., (), -
##[10]
S. Kakutani, A generalization of Brouwer's fixed point theorem, Duke Math. J., 8 (1941), 457-459
##[11]
E. Karapınar, I. M. Erhan, Fixed point theorems for operators on partial metric spaces, Appl. Math. Lett., 24 (2011), 1894-1899
##[12]
E. Karapınar, M. A. Kutbi, H. Piri, D. O'Regan, Fixed points of conditionally F-contractions in complete metric- like spaces, Fixed Point Theory and Appl., 2015 (2015), 1-14
##[13]
S. G. Matthews, Partial metric topology, Research Report 212, Dept. of Computer Science, University ofWarwick (1992)
##[14]
S. G. Matthews, Partial metric topology, Papers on general topology and applications, Proc. 8th Summer Conf., Queen's College, (1992), Ann. New York Acad. Sci., New York Acad. Sci., New York, 1994 (1994), 183-197
##[15]
S. Moradi, A. Farajzadeh, On the fixed point of ( \(\psi-\phi\))-weak and generalized (\(\psi-\phi\))-weak contraction mappings, Appl. Math. Lett., 25 (2012), 1257-1262
##[16]
X.-H. Mu, C.-X. Zhu, Z.-Q. Wu, New multipled common fixed point theorems in Menger PM-spaces, Fixed Point Theory and Appl., 2015 (2015), 1-9
##[17]
S. Oltra, O. Valero, Banach's fixed point theorem for partial metric spaces, Rend. Istit. Mat. Univ. Trieste, 36 (2004), 17-26
##[18]
S. J. O'Neill, Partial metrics, valuations, and domain theory, Papers on general topology and applications, Gorham, ME, (1995), 304-315, Ann. New York Acad. Sci., New York Acad. Sci., New York (1996)
##[19]
H. Piri, P. Kuman, Some fixed point theorems concerning F-contraction in complete metric spaces, Fixed Point Theory and Appl., 2014 (2014), 1-11
##[20]
D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory and Appl., 2012 (2012), 1-6
##[21]
D. Wardowski, N. Van Dung, Fixed points of F-weak contractions on complete metric spaces, Demonstr. Math., 47 (2014), 146-155
##[22]
C.-X. Zhu, Research on some problems for nonlinear operators, Nonlinear Anal., 71 (2009), 4568-4571
]
Almost \(e^*\)-continuous functions and their characterizations
Almost \(e^*\)-continuous functions and their characterizations
en
en
The main goal of this paper is to introduce and investigate a new class of functions called almost
\(e^*\)-continuous functions containing the class of almost e-continuous functions defined by Özkoçand
Kına. Several characterizations concerning almost \(e^*\)-continuous functions are obtained. Furthermore,
we investigate the relationships between almost \(e^*\)-continuous functions and separation axioms
and almost \(e^*\)-closedness of graphs of functions.
6408
6423
Burcu Sünbül
Ayhan
Faculty of Science, Department of Mathematics
Mugla Sitki Kocman University
Turkey
brcyhn@gmail.com
Murad
Özkoç
Faculty of Science, Department of Mathematics
Mugla Sitki Kocman University
Italy
murad.ozkoc@mu.edu.tr
\(e^*\)-open
\(e^*\)-continuity
almost \(e^*\)-continuity
weakly \(e^*\)-continuity
faintly \(e^*\)-continuity
\(e^*\)-closed graph.
Article.40.pdf
[
[1]
D. Andrijević, On b-open sets, Mat. Vesnik, 48 (1996), 59-64
##[2]
E. Ekici, New forms of contra-continuity, Carpathian J. Math., 24 (2008), 37-45
##[3]
E. Ekici, On a-open sets,\( A^*\)-sets and decompositions of continuity and super-continuity, Ann. Univ. Sci. Budapest. Eötvös Sect. Math., 51 (2008), 39-51
##[4]
E. Ekici, On e-open sets, \(DP^*\)-sets and \(DPE^*\)-sets and decompositions of continuity, Arab. J. Sci. Eng. Sect. A Sci., 33 (2008), 269-282
##[5]
E. Ekici, On \(e^*\)-open sets and \((D; S)^*\)-sets, Math. Morav., 13 (2009), 29-36
##[6]
E. Ekici, Some weak forms of \(\delta\)-continuity and \(e^*\)-first-countable spaces, (submitted), (), -
##[7]
N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly, 70 (1963), 36-41
##[8]
A. S. Mashhour, M. E. Abd El-Monsef, S. N. El-Deeb, On precontinuous and weak precontinuous mappings, Proc. Math. Phys. Soc. Egypt, 53 (1982), 47-53
##[9]
O. Njastad, On some classes of nearly open sets, Pacific J. Math., 15 (1965), 961-970
##[10]
T. Noiri, Almost quasi-continuous functions, Bull. Inst. Math. Acad. Sinica, 18 (1990), 321-332
##[11]
T. Noiri, V. Popa, On almost \(\beta\)-continuous functions, Acta Math. Hungar., 79 (1998), 329-339
##[12]
M. Özkoç, H. Kına, On almost e-continuous functions, (submitted), (), -
##[13]
J. H. Park, B. Y. Lee, M. J. Son, On \(\delta\)-semiopen sets in topological space, J. Indian Acad. Math., 19 (1997), 59-67
##[14]
S. Raychaudhuri, M. N. Mukherjee, On \(\delta\)-almost continuity and \(\delta\)-preopen sets, Bull. Inst. Math. Acad. Sinica, 21 (1993), 357-366
##[15]
U. Şengül, On almost b-continuous functions, Int. J. Contemp. Math. Sci., 3 (2008), 1469-1480
##[16]
M. K. Singal, S. Prabha Arya, On almost-regular spaces, Glasnik Mat. Ser. III, 4 (1969), 89-99
##[17]
M. K. Singal, A. R. Singal, Almost-continuous mappings, Yokohama Math. J., 16 (1968), 63-73
##[18]
M. H. Stone, Applications of the theory of Boolean rings to general topology, Trans. Amer. Math. Soc., 41 (1937), 375-381
##[19]
S. S. Thakur, P. Paik, Almost \(\alpha\)-continuous mappings, J. Sci. Res., 9 (1987), 37-40
##[20]
N. V. Veličko, H-closed topological spaces, Amer. Math. Soc. Transl., 78 (1968), 103-118
]