]>
2019
12
10
ISSN 2008-1898
77
Hybrid iterative methods for two asymptotically nonexpansive semigroups in Hilbert spaces
Hybrid iterative methods for two asymptotically nonexpansive semigroups in Hilbert spaces
en
en
The main objective of this work is to modify two hybrid projection algorithm. First, we prove the strongly convergence to common fixed points of a sequence \(\{x_{n}\}\) generated by the hybrid projection algorithm of two asymptotically nonexpansive mappings, second, we prove the strongly convergence of a sequence \(\{x_{n}\}\) generated by the hybrid projection algorithm of two asymptotically nonexpansive semigroups. Our main results extend and improve the results of Dong et al. [Q.-L. Dong, S. N. He, Y. J. Cho, Fixed Point Theory Appl., \(\textbf{2015}\) (2015), 12 pages].
621
633
Issara
Inchan
Department of Mathematics
Uttaradit Rajabhat University
Thailand
peissara@uru.ac.th
Asymptotically nonexpansive mappings
asymptotically nonexpansive semigroup
fixed point
Article.1.pdf
[
[1]
Q.-L. Dong, S. N. He, Y. J. Cho, A new hybrid algorithm and numerical realization for two nonexpansive mappings, Fixed Point Theory Appl., 2015 (2015), 1-12
##[2]
K. Goebel, W. A. Kirk, A fixed point theorem for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc., 35 (1972), 171-174
##[3]
I. Inchan, S. Plubtieng, Strong convergence theorems of hybrid methods for two asymptotically nonexpansive mappings in Hilbert spaces, Nonlinear Anal. Hybrid Syst., 2 (2008), 1125-1135
##[4]
S. Ishikawa, Fixed points by a new iteration method, Proc. Amer. Math. Soc., 44 (1974), 147-150
##[5]
T.-H. Kim, H.-K. Xu, Strong convergence of modified Mann iterations for asymptotically nonexpansive mappings and semigroups, Nonlinear. Anal., 64 (2006), 1140-1152
##[6]
P.-K. Lin, K.-K. Tan, H. K. Xu, Demiclosedness principle and asymptotic behavior for asymptotically nonexpansive mappings, Nonlinear. Anal., 24 (1995), 929-946
##[7]
W. A. Mann, Mean value methods in iteration, Proc. Amer. Math. Soc., 4 (1953), 506-510
##[8]
C. Martinez-Yanes, H.-K. Xu, Strong convergence of the CQ method for fixed point processes, Nonlinear Anal., 64 (2006), 2400-2411
##[9]
Z. Opial, Weak convergence of the sequence of successive approximations for nonexpansive mappings, Bull. Amer. Math. Soc., 73 (1967), 591-597
##[10]
J. Schu, Weak and strong convergence to fixed points of asymptotically nonexpansive mappings, Bull. Amer. Math. Soc., 43 (1991), 153-159
##[11]
W. Takahashi, Y. Takeuchi, R. Kubota, Strong convergence theorems by hybrid methods for families of nonexpansive mappings in Hilbert spaces, J. Math. Anal. Appl., 341 (2008), 276-286
##[12]
H.-K. Xu, Strong asymptotic behavior of almost-orbits of nonlinear semigroups, Nonlinear. Anal., 46 (2001), 135-151
]
\(O_1\)-convergence in partially ordered sets
\(O_1\)-convergence in partially ordered sets
en
en
Based on the introduction of notions of \(S^*\)-doubly continuous posets and
B-topology in [T. Sun, Q. G. Li, L. K. Guo, Topology Appl., \(\bf207\) (2016), 156--166], in this paper, we further propose the
concept of B-consistent \(S^*\)-doubly
continuous posets and prove that the
\(O_1\)-convergence in a poset is topological if and only if the poset is a
B-consistent \(S^*\)-doubly continuous poset. This is the main result which
can be seen as a sufficient and necessary condition for the \(O_1\)-convergence in
a poset being topological. Additionally, in order to present natural examples
of posets which satisfy such condition, several special sub-classes of
B-consistent \(S^*\)-doubly continuous posets are investigated.
634
643
Tao
Sun
College of Mathematics and Physics
College of Mathematics and Econometrics
Hunan University of Arts and Science
Hunan University
P. R. China
P. R. China
suntao5771@163.com
Qingguo
Li
College of Mathematics and Econometrics
Hunan University
P. R. China
liqingguoli@aliyun.com
Nianbai
Fan
College of Computer Science and Electronic Engineering
Hunan University
P. R. China
nbfan6203@163.com
\(O_1\)-convergence
B-topology
\(S^*\)-doubly continuous poset
B-consistent \(S^*\)-doubly continuous poset
Article.2.pdf
[
[1]
G. Birkhoff, Lattice Theory, American Mathematical Society, New York (1940)
##[2]
M. M. Dai, H. Y. Chen, D. W. Zheng, An introduction to axiomatic set theory (in chinese), Science Press, Beijing (2011)
##[3]
B. A. Davey, H. A. Priestley, Introduction to Lattices and Order, Cambridge University Press, Cambridge (2002)
##[4]
R. Engelking, General Topology, PWN-Polish Scientific Publishers, Warszawa (1977)
##[5]
O. Frink, Topology in lattice, Trans. Amer. Math. Soc., 51 (1942), 569-582
##[6]
G. Grierz, K. H. Hofmann, K. Keimel, J. D. Lawson, M. W. Mislove, D. S. Scott, Continuous Lattices and Domain, Camberidge University Press, Camberidge (2003)
##[7]
J. L. Kelly, General Topology, Van Nostrand, New York (1955)
##[8]
J. C. Mathews, R. F. Anderson, A comparison of two modes of order convergence, Proc. Amer. Math. Soc., 18 (1967), 100-104
##[9]
E. J. Mcshane, Order--Preserving Maps and Integration Processes, Princeton University Press, Princeton (1953)
##[10]
V. Olejček, Order Convergence and Order Topology on a Poset, Internat. J. Theoret. Phys., 38 (1999), 557-561
##[11]
Z. Riečanová, Strongly compactly atomistic orthomodular lattices and modular ortholattices, Tatra Mt. Math. Publ., 15 (1998), 143-153
##[12]
T. Sun, Q. G. Li, L. K. Guo, Birkhoff's order--convergence in partially ordered sets, Topology Appl., 207 (2016), 156-166
##[13]
K. Y. Wang, B. Zhao, Some further result on order--convergence in posets, Topology Appl., 160 (2013), 82-86
##[14]
E. S. Wolk, On order--convergence, Proc. Amer. Math. Soc., 12 (1961), 379-384
##[15]
H. Zhang, A note on continuous partially ordered sets, Semigroup Forum, 47 (1993), 101-104
##[16]
D. S. Zhao, The double Scott topology on a lattice, Chin. Ann. Math. Ser. A, 10 (1989), 187-193
##[17]
B. Zhao, K. Y. Wang, Order topology and bi-Scott topology on poset, Acta Math. Sin. (Engl. Ser.), 27 (2011), 2101-2106
##[18]
B. Zhao, D. S. Zhao, Lim--inf--convergence in partially ordered sets, J. Math. Anal. Appl., 309 (2005), 701-708
##[19]
Y. H. Zhou, B. Zhao, Order--convergence and Lim--inf$_{\mathcal{M}}$--convergence in poset, J. Math. Anal. Appl., 325 (2007), 655-664
]
Common fixed point of generalized cyclic Banach algebra contractions and Banach algebra Kannan types of mappings on cone quasi metric spaces
Common fixed point of generalized cyclic Banach algebra contractions and Banach algebra Kannan types of mappings on cone quasi metric spaces
en
en
This paper proves the existence of a unique common fixed point of two self mappings defined on complete cone quasi metric space \(\mathfrak{C}\) with respect to Banach algebra, consequently in particular, it proves the existence of only one fixed point of a generalized cyclic Banach algebra contraction and a cyclic Banach algebra Kannan type mappings with respect to a couple of non empty subsets \((A, B)\) of a complete cone quasi metric space \(\mathfrak{C}\). These existences extend the fixed point results of the attached references and then generalized the corresponding classical results in usual Banach spaces as well.
644
655
Sahar Mohamed Ali
Abou Bakr
Department of Mathematics, Faculty of Science
Ain Shams University
Egypt
saharm_ali@yahoo.com
Quasi metric spaces
fixed point theorems
\(\{a,b,c\}\) generalized contractions
generalized \(\phi\) weak contractions
cyclic contraction mappings
Article.3.pdf
[
[1]
M. Abbas, V. Ćojbašić Rajić, T. Nazir, S. Radenović, Common fixed point of mappings satisfying rational inequalities in ordered complex valued generalized metric spaces, Afr. Mat., 26 (2015), 17-30
##[2]
S. M. Ali, Fixed point theorems of $\{a, b, c\}$ contraction and nonexpansive type mappings in weakly Cauchy normed spaces, Anal. Theory Appl., 29 (2013), 280-288
##[3]
S. M. Ali Abou Bakr, Some Generalized Fixed Point Theorems of Contraction Type Mappings in Quasi Metric Spaces, J. Math. Stat., 14 (2017), 319-324
##[4]
H. Aydi, E. Karapinar, B. Samet, Remarks on some recent fixed point theorems, Fixed Point Theory Appl., 2012 (2012), 1-6
##[5]
H. Çakally, A. Sönmez, Ç. Genç, On an equivalence of topological vector space valued cone metric spaces and metric spaces, Appl. Math. Lett., 25 (2012), 429-433
##[6]
W.-S. Du, A note on cone metric fixed point theory and its equivalence, Nonlinear Anal., 72 (2010), 2259-2261
##[7]
P. N. Dutta, B. S. Choudhury, A generalisation of contraction principle in metric spaces, Fixed Point Theory Appl., 2008 (2008), 1-8
##[8]
E. El-Shobaky, S. M. Ali, M. S. Ali, Generalization of Banach contraction principle in two directions, J. Math. Stat., 3 (2007), 112-115
##[9]
J. Fernandez, N. Malviya, S. Radenovič, K. Saxena, $F$--cone metric spaces over Banach algebra, Fixed Point Theory Appl., 2017 (2017), 1-18
##[10]
J. Fernandez, G. Modi, N. Malviya, Some fixed point theorems for contractive maps in N-cone metric spaces, Math. Sci. (Springer), 9 (2015), 33-38
##[11]
J. Fernandez, K. Saxena, N. Malviya, Fixed points of expansive maps in partial cone metric spaces, Gazi University J. Sci., 27 (2014), 1085-1091
##[12]
R. George, H. A. Nabwey, R. Rajagopalan, S. Radenovič, K. P. Reshma, Rectangular cone $b$--metric spaces over Banach algebra and contraction principle, Fixed Point Theory Appl., 2017 (2017), 1-15
##[13]
R. H. Haghi, S. Rezapour, N. Shahzad, Some fixed point generalizations are not real generalizations, Nonlinear Anal., 74 (2011), 1799-1803
##[14]
R. H. Haghi, S. Rezapour, N. Shahzad, Be careful on partial metric fixed point results, Topology Appl., 160 (2013), 450-454
##[15]
H. P. Huang, S. Radenovič, Some fixed point results of generalised Lipschitz mappings on cone b-metric spaces over Banach algebras, J. Comput. Anal. Appl., 20 (2016), 566-583
##[16]
L.-G. Huang, X. Zhang, Cone metric spaces and fixed point theorem of contractive mappings, J. Math. Anal. Appl., 332 (2007), 1468-1476
##[17]
W. A. Kirk, P. S. Srinivasan, P. Veeramani, Fixed points for mappings satisfying cyclical contractive conditions, Fixed Point Theory, 4 (2003), 79-89
##[18]
H. Liu, S. Y. Xu, Cone metric spaces with Banach algebras and fixed point theorems of generalized Lipschitz mappings, Fixed Point Theory Appl., 2013 (2013), 1-10
##[19]
N. Malviya, B. Fisher, $N$--cone metric space and fixed points of asymptotically regular maps, Filomat, 2013 (2013), 1-11
##[20]
W. Rudin, Functional Analysis, McGraw-Hill, New York (1991)
##[21]
N. Sharma, Fixed point theorem in cone $B$--metric spaces using contractive mappings, Global J. Pure Appl. Math., 13 (2017), 2997-3004
]
A Fourier transform and convolution of Diamond operator
A Fourier transform and convolution of Diamond operator
en
en
In this paper, we define a new operator and give a sense of distribution theory to find the Fourier transform of new operator. It was found that
the Fourier transform of new operator related to the Fourier transform of ultrahyperbolic operator and Diamond operator. And we also study the convolution products
\(\Box^{k}\delta \ast \Box^{l}\) and \(\diamondsuit^{k}\delta\ast \diamondsuit^{l}.\)
656
666
Wanchak
Satsanit
Department of Mathematics, Faculty of Science
Maejo University
Thailand
wanchack@gmail.com
Diamond operator
Fourier transform
hypersurface
Article.4.pdf
[
[1]
M. A. Aguirre Tellez, A. Kananthai, On the convolution product of the Distributional Families related to the Diamond operator, Matematiche (Catania), 57 (2002), 39-48
##[2]
M. A. Aguirre Tellez, S. E. Trione, The distribution Multiplicative product $P^{-\frac{s}{2}}_{\pm}\delta(x)$, Rev. Colombiana Mat., 27 (1993), 1-7
##[3]
I. M. Gel'fand, G. E. Shilov, Generalized Function , (Translated from the Russian by Eugene Saletan), Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London (1964)
##[4]
A. González Domínguez, S. E. Trione, On the Laplace transform of retarded Lorentz invariant functions, Adv. in Math., 31 (1979), 51-62
##[5]
A. Kananthai, On the Solution of the $n$-Dimensional Diamond Operator, Appl. Math. Comput., 88 (1997), 27-37
##[6]
A. Kananthai, On the Fourier transform of the Diamond kernel of Marcel Riesz, Appl. Math. Comput., 101 (1999), 151-158
##[7]
A. Kananthai, K. Nonlaopon, On the Residue of Generalized Function $P^{\lambda}$, Thai J. Math., 1 (2003), 49-57
##[8]
K. Nonlaopon, M. Aguirre Tellez, The Residue of the Generalized function $P^{\lambda}_{+}$ in hypercone $P=(ar)^{2}-(br)^{2}$, to appear, (), -
##[9]
Y. Nozaki, On Riemann-Liouville integral of ultra--hyperbolic type, Kodai Math. Sem. Rep., 16 (1964), 69-87
##[10]
S. E. Trione, M. A. Aguirre Tellez, The distribution convolution products of Marcel Riesz's ultra-hyperbolic kernel, Ravista de la Union Mathematica Argentina, 39 (1995), 115-124
]
Fixed point theorems for \(\Theta\)-contractions in left \(K\)-complete \(T_{1}\)-quasi metric space
Fixed point theorems for \(\Theta\)-contractions in left \(K\)-complete \(T_{1}\)-quasi metric space
en
en
The aim of this paper is to define \(\Theta
_{\beta }^{u}=\left \{ v\in \mathcal{J}u:\Theta (\varrho (u,v))\leq \lbrack
\Theta (\varrho (u,\mathcal{J}u))]^{\beta }\right \} \) and establish some
new fixed point theorems in the setting of left \(K\)-complete \(T_{1}\)-quasi
metric space. Our theorems generalize, extend, and unify several results of
literature.
667
674
Durdana
Lateef
Department of Mathematics, College of Science
Taibah University
Kingdom of Saudi Arabia
drdurdanamaths@gmail.com
Jamshaid
Ahmad
Department of Mathematics
University of Jeddah
Saudi Arabia
jkhan@uj.edu.sa
\(\Theta\)-contractions
property \(P\)
property \(Q\)
fixed points
Article.5.pdf
[
[1]
M. Abbas, B. Ali, S. Romaguera, Fixed and periodic points of generalized contractions in metric spaces, Fixed Point Theory Appl., 2013 (2013), 1-11
##[2]
J. Ahmad, A. Al-Rawashdeh, A. Azam, New fixed point theorems for generalized $F$-contractions in complete metric spaces, Fixed Point Theory Appl., 2015 (2015), 1-18
##[3]
A. Al-Rawashdeh, J. Ahmad, Common Fixed Point Theorems for JS-Contractions, Bull. Math. Anal. Appl., 8 (2016), 12-22
##[4]
I. Altun, B. Damjanović, D. Djorić, Fixed point and common fixed point theorems on ordered cone metric spaces, Appl. Math. Lett., 23 (2010), 310-316
##[5]
S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fundam. Math., 3 (1922), 133-181
##[6]
I. Beg, M. Abbas, Coincidence point and invariant approximation for mappings satisfying generalized weak contractive condition, Fixed Point Theory Appl., 2006 (2006), 1-7
##[7]
H. Dağ, G. Minak, I. Altun, Some fixed point results for multivalued $F$--contractions on quasi metric spaces, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM, 111 (2017), 177-187
##[8]
H. A. Hançer, G. Minak, I. Altun, On a broad category of multivalued weakly Picard operators, Fixed Point Theory, 18 (2017), 229-236
##[9]
N. Hussain, J. Ahmad, L. Ćirić, A. Azam, Coincidence point theorems for generalized contractions with application to integral equations, Fixed Point Theory Appl., 2015 (2015), 1-13
##[10]
N. Hussain, V. Parvaneh, B. Samet, C. Vetro, Some fixed point theorems for generalized contractive mappings in complete metric spaces, Fixed Point Theory Appl., 2015 (2015), 1-17
##[11]
G. S. Jeong, B. E. Rhoades, Maps for which $F(T)=F(T^{n})$, In: Fixed Point Theory and Applications, Nova Science Publishers, 2007 (2007), 71-105
##[12]
M. Jleli, B. Samet, A new generalization of the Banach contraction principle, J. Inequal. Appl., 2014 (2014), 1-8
##[13]
G. Jungck, Commuting mappings and fixed points, Amer. Math. Monthly, 83 (1976), 261-263
##[14]
G. Jungck, Compatible mappings and common fixed points, Internat. J. Math. Math. Sci., 9 (1986), 771-779
##[15]
B. Samet, C. Vetro, P. Vetro, Fixed point theorem for $\alpha -\psi $ contractive type mappings, Nonlinear Anal., 75 (2012), 2154-2165
##[16]
F. Vetro, A generalization of Nadler fixed point theorem, Carpathian J. Math., 31 (2015), 403-410
]
A higher order nonlinear neutral differential equation
A higher order nonlinear neutral differential equation
en
en
This paper is concerned with the higher order nonlinear neutral
differential equation
\[
[a(t)(x(t)+b(t)x(\tau(t)))']^{(n-1)}+f(t, x(g_1(t)),\ldots,
x(g_k(t)))=c(t),\quad t\ge t_0.
\]
By dint of the Leray-Schauder nonlinear alternative, Rothe fixed
point theorem and some new techniques, we prove the existence of
uncountably many bounded positive solutions for the equation.
Several nontrivial examples are given to illustrate the
applications and advantages of the results presented in this
paper.
675
698
Guojing
Jiang
Basic Teaching Department
Vocational Technical College
China
jiangguojing@qq.com
Wei
Sun
Jiaokou No.1 Middle School
China
weisun_dl@163.com
Zhefu
An
School of Mathematics
Liaoning University
China
zhefuan@163.com
Liangshi
Zhao
Center for Studies of Marine Economy and Sustainable Development
Liaoning Normal University
China
liangshizhao85@163.com
Higher order nonlinear neutral differential equation
uncountably many bounded positive solutions
Leray-Schauder nonlinear alternative theorem
Rothe fixed point theorem
Article.6.pdf
[
[1]
R. P. Agarwal, S. R. Grace, D. O'Regan, Nonoscillatory solutions for discrete equations, Comput. Math. Appl., 45 (2003), 1297-1302
##[2]
K. Deimling, Nonlinear Functional Analysis, Springer-Verlag, Berlin (1985)
##[3]
Z. Liu, H. Gao, S. M. Kang, S. H. Shim, Existence and mann iterative approximations of nonoscillatory solutions of nth order neutral delay differential equations, J. Math. Anal. Appl., 329 (2007), 515-529
##[4]
Z. G. Zhang, A. J. Yang, C. N. Di, Existence of positive solutions of second order nonlinear neutral differential equations with positive and negative terms, J. Appl. Math. Comput., 25 (2007), 245-253
##[5]
Y. Zhou, Existence for nonoscillatory solutions of second order nonlinear differential equations, J. Math. Anal. Appl., 331 (2007), 91-96
##[6]
X. L. Zhou, R. Yu, Oscillatory behavior of higher order nonlinear neutral forced differential equations with oscillating coefficients, Comput. Math. Anal., 56 (2008), 1562-1568
##[7]
Y. Zhou, B. G. Zhang, Y. Q. Huang, Existence for nonoscillatory solutions of higher order nonlinear neutral differential equations, Czechoslovak Math. J., 55 (2005), 237-253
]