]>
2015
8
5
ISSN 2008-1898
448
Extended Riemann-Liouville fractional derivative operator and its applications
Extended Riemann-Liouville fractional derivative operator and its applications
en
en
Many authors have introduced and investigated certain extended fractional derivative operators. The main
object of this paper is to give an extension of the Riemann-Liouville fractional derivative operator with
the extended Beta function given by Srivastava et al. [22] and investigate its various (potentially) useful
and (presumably) new properties and formulas, for example, integral representations, Mellin transforms,
generating functions, and the extended fractional derivative formulas for some familiar functions.
451
466
Praveen
Agarwal
Department of Mathematics
Anand International College of Engineering
India
goyal.praveen2011@gmail.com
Junesang
Choi
Department of Mathematics
Dongguk University
Republic of Korea
junesang@mail.dongguk.ac.kr
R. B.
Paris
School of Computing, Engineering and Applied Mathematics
University of Abertay Dundee
UK
r.paris@abertay.ac.uk
Gamma function
Beta function
Riemann-Liouville fractional derivative
hypergeometric functions
fox H-function
generating functions
Mellin transform
integral representations.
Article.1.pdf
[
[1]
R. Almeida, D. F. M. Torres, Necessary and sufficient conditions for the fractional calculus of variations with Caputo derivatives, Nonlinear Sci. Numer. Simul., 16 (2011), 1490-1500
##[2]
L. M. B. C. Campos, On a concept of derivative of complex order with application to special functions, IMA J. Appl. Math., 33 (1984), 109-133
##[3]
L. M. B. C. Campos, On rules of derivation with complex order of analytic and branched functions, Portugal. Math., 43 (1985), 347-376
##[4]
L. M. B. C. Campos, On a systematic approach to some properties of special functions, IMA J. Appl. Math., 36 (1986), 191-206
##[5]
M. A. Chaudhry, S. M. Zubair, On a Class of Incomplete Gamma Functions with Applications, Chapman and Hall (CRC Press Company), Boca Raton, London, New York and Washington, D.C. (2001)
##[6]
M. A. Chaudhry, A. Qadir, M. Rafique, S. M. Zubair, Extension of Euler’s beta function, J. Comput. Appl. Math., 78 (1997), 19-32
##[7]
M. A. Chaudhry, A. Qadir, H. M. Srivastava, R. B. Paris, Extended hypergeometric and confluent hypergeometric functions, Appl. Math. Comput., 159 (2004), 589-602
##[8]
A. A. Kilbas, M. Saigo, H-Transforms: Theory and Applications, Chapman and Hall (CRC Press Company), Boca Raton, London, New York and Washington, D.C. (2004)
##[9]
A. A. Kilbas, H. M. Srivastava, J. J. Trujillo, Theory and Applications of Fractional Differential Equations, in: North-Holland Mathematics Studies, vol. 204, Elsevier Science B.V., Amsterdam (2006)
##[10]
V. Kiryakova , Generalized Fractional Calculus and Applications, Longman & J. Wiley, Harlow-New York (1994)
##[11]
C. Li, A. Chen, J. Ye, Numerical approaches to fractional calculus and fractional ordinary differential equation, J. Comput. Physics, 230 (2011), 3352-3368
##[12]
M. J. Luo, G. V. Milovanovic, P. Agarwal , Some results on the extended beta and extended hypergeometric functions, Appl. Math. Comput., 248 (2014), 631-651
##[13]
J. T. Machado, V. Kiryakova, F. Mainardi, Recent history of fractional calculus, Commun. Nonlinear Sci. Numer. Simulat., 16 (2011), 1140-1153
##[14]
R. L. Magin, Fractional calculus models of complex dynamics in biological tissues, Comput. Math. Appl., 59 (2010), 1586-1593
##[15]
A. M. Mathai, R. K. Saxena, H. J. Haubold, The H-function: Theory and applications, Springer, New York (2010)
##[16]
A. R. Miller, Remarks on a generalized beta function, J. Comput. Appl. Math., 100 (1998), 23-32
##[17]
P. A. Nekrassov, General differentiation, Mat. Sbornik, 14 (1888), 45-168
##[18]
T. J. Osler, Leibniz rule for the fractional derivatives and an application to infinite series, SIAM J. Appl. Math., 18 (1970), 658-674
##[19]
T. J. Osler, Leibniz rule, the chain rule and Taylor’s theorem for fractional derivatives, Ph.D. thesis, New York University (1970)
##[20]
M. A. Özarslan, E. Özergin, Some generating relations for extended hypergeometric functions via generalized fractional derivative operator, Math. Comput. Model., 52 (2010), 1825-1833
##[21]
E. Özergin, M. A. Özarslan, A. Altin, Extension of gamma, beta and hypergeometric functions, J. Comput. Appl. Math., 235 (2011), 4601-4610
##[22]
H. M. Srivastava, P. Agarwal, S. Jain, Generating functions for the generalized Gauss hypergeometric functions, Appl. Math. Comput., (document). , 247 (2014), 348-352
##[23]
H. M. Srivastava, J. Choi , Zeta and q-Zeta Functions and Associated Series and Integrals, Elsevier Science Publishers, Amsterdam, London and New York (2012)
##[24]
H. M. Srivastava, H. L. Manocha, A Treatise on Generating Functions, Halsted Press (Ellis Horwood Limited, Chichester), John Wiley and Sons, New York, Chichester, Brisbane and Toronto (1984)
##[25]
J. Zhao, Positive solutions for a class of q-fractional boundary value problems with p-Laplacian, J. Nonlinear Sci. Appl., 8 (2015), 442-450
]
Singularity properties of one parameter lightlike hypersurfaces in Minkowski 4-space
Singularity properties of one parameter lightlike hypersurfaces in Minkowski 4-space
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en
In this paper, we give one parameter families of extrinsic differential geometries on spacelike curves in
Minkowski 4-space. We investigate the nonlinear properties of one parameter lightlike hypersurfaces. Meanwhile,
the classification of singularities to one parameter lightlike hypersurfaces is considered by singularity
theory.
467
477
Jianguo
Sun
School of Science
China University of Petroleum (east China)
P. R. China
sunjg616@163.com
Donghe
Pei
School of Mathematics and Statistics
Northeast Normal University
P. R. China
peidh340@nenu.edu.cn
Minkowski space
singularity
one parameter lightlike hypersurfaces
height function.
Article.2.pdf
[
[1]
A. Bruce, Vacuum states in de Sitter space, Phys. Rev. D, 32 (1985), 3136-3149
##[2]
J. W. Bruce, P. J. Giblin, Curves and singularities (2nd. ed.) , Cambridge Univ. Press, Cambridge (1992)
##[3]
M. Campanelli, C. O. Lousto, Second order gauge invariant gravitational perturbations of a Kerr black hole, Phys. Rev. D, 59 (1999), 1-16
##[4]
S. Coleman, R. E. Nirton , Sigularities in the physical region, Il. Nuovo. Cimento., 38 (1965), 438-442
##[5]
K. L. Duggal, D. H. Jin , Null curves and hypersurfaces of semi-Riemannian manifolds, World Scientific, (2007)
##[6]
T. Fusho, S. Izumiya, Lightlike surfaces of spacelike curves in de Sitter 3-space, J. Geom., 88 (2008), 19-29
##[7]
W. A. Hiscock, Models of evaporating black holes. II. Effects of the outgoing created radiation, Phys. Rev. D, 23 (1981), 2823-2827
##[8]
K. Ilarslan, Ö. Boyacıoğlu, Position vectors of a timelike and a null helix in Minkowski 3-space , Chaos Solitons Fractals, 38 (2008), 1383-1389
##[9]
B. Mustafa, On the involutes of the spacelike curve with a timelike binormal in Minkowski 3-space, Internat. Math. Forum, 31 (2009), 1497-1509
##[10]
B. O'Neill , Semi-Riemannian geomerty with applications to relativity, Academic Press, London (1983)
##[11]
A. Neraessian, E. Ramos, Massive spinning particles and the geometry of null curves, Phys. Lett. B, 445 (1998), 123-128
##[12]
D. H. Pei, T. Sano, The focal developable and the binormal indicatrix of a nonlightlike curve in Minkowski 3-space, Tokyo J. Math., 23 (2000), 211-225
##[13]
J. G. Sun, D. H. Pei , Families of Gauss indicatrices on Lorentzian hypersurfaces in pseudo-spheres in semi- Euclidean 4 space, J. Math. Anal. Appl., 400 (2013), 133-142
##[14]
J. G. Sun, D. H. Pei, Null surfaces of null curves on 3-null cone, Phys. Lett. A, 378 (2014), 1010-1016
##[15]
J. G. Sun, D. H. Pei, Some new properties of null curves on 3-null cone and unit semi-Euclidean 3-spheres, J. Nonlinear Sci. Appl., 8 (2015), 275-284
##[16]
G. H. Tian, Z. Zhao, C. B. Liang , Proper acceleration’ of a null geodesic in curved spacetime, Classical Quantum Gravity, 20 (2003), 1-4329
##[17]
H. Urbantke , Local differential geometry of null curves in conformally flat space-time , J. Math. Phys., 30 (1989), 2238-2245
]
A novel solution for fractional chaotic Chen system
A novel solution for fractional chaotic Chen system
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en
A novel solution to the fraction chaotic Chen system is presented in this paper by using the step homotopy
analysis method. This method yields a continuous solution in terms of a rapidly convergent infinite power
series with easily computable terms. Moreover, the residual error of the SHAM solution is defined and
computed for each time interval. Via the computing of the residual error we observe that the accuracy of
the present method tends to \(10^{-11}\) which is very high.
478
488
A. K.
Alomari
Department of Mathematics, Faculty of Science
Yarmouk University
Jordan
abdomari2008@yahoo.com
Chaotic system
fractional Chen system
homotopy analysis method
step homotopy analysis method
residual error.
Article.3.pdf
[
[1]
S. Abbasbandy, The application of homotopy analysis method to solve a generalized Hirota-Satsuma coupled KdV equation, Phys. Lett. A, 361 (2007), 478-483
##[2]
A. K. Alomari, M. S. M. Noorani, R. Nazar, On the homotopy analysis method for the exact solutions of Helmholtz equation, Chaos Solitons Fractal, 41 (2009), 1873-1879
##[3]
A. K. Alomari, F. Awawdeh, N. Tahat, F. Bani Ahmad, W . Shatanawi , Multiple solutions for fractional differential equations: Analytic approach, Appl. Math. Comput., 219 (2013), 8893-8903
##[4]
A. K. Alomari, M. S. N. Noorani, R. Nazar, Adaptation of homotopy analysis method for the numeric-analytic solution of Chen system, Comm. Nonlinear Sci. Numer. Simul., 14 (2009), 2336-2346
##[5]
A. K. Alomari, M. S. N. Noorani, R. Nazar, C. P. Li, Homotopy analysis method for solving fractional Lorenz system, Comm. Nonlinear Sci. Numer. Simul., 15 (2010), 1864-1872
##[6]
M. A. F. Araghi, A. Fallahzadeh, Discrete Homotopy Analysis Method for Solving Linear Fuzzy Differential Equations, Adv. Environ. Biol., 9 (2015), 195-201
##[7]
A. S. Bataineh, M. S. N. Noorani, I. Hashim, Solving systems of ODEs by homotopy analysis method , Comm. Nonlinear Sci. Numer. Simul., 13 (2008), 2060-2070
##[8]
M. S. H. Chowdhury, I. Hashim, Application of multistage homotopy-perturbation method for the solutions of the Chen system , Nonlinear Anal. Real. World Appl., 10 (2009), 381-391
##[9]
K. Diethelm, N. J. Ford, Analysis of fractional differential equations, J. Math. Anal. Appl., 265 (2002), 229-248
##[10]
K. Diethelm, N. J. Ford, A. D. Freed, A predictor-corrector approach for the numerical solution of fractional differential equations, Nonlinear Dyn., 29 (2002), 3-22
##[11]
A. Fallahzadeh, K. Shakibi, A method to solve Convection-Diffusion equation based on homotopy analysis method, J. Interpolat. Approx. Sci. Comput., 2015 (2015), 1-8
##[12]
A. Golbabai, K. Sayevand , An efficient applications of hes variational iteration method based on a reliable modification of Adomian algorithm for nonlinear boundary value problems , J. Nonlinear Sci. Appl., 3 (2010), 152-156
##[13]
T. Hayat, M. Sajid, On analytic solution for thin film flow of a fourth grade fluid down a vertical cylinder, Phys. Lett. A, 361 (2007), 316-322
##[14]
T. Hayat, M. Khan, Homotopy solutions for a generalized second-grade fluid past a porous plate, Nonlinear Dyn., 42 (2005), 395-405
##[15]
H. Jafari, V. Daftardar-Gejji , Solving a system of nonlinear fractional differential equations using Adomian decomposition, J. Comput. Appl. Math., 196 (2006), 644-651
##[16]
C. Li C, G. Peng, Chaos in Chen’s system with a fractional order, Chaos Solitons Fractals, 22 (2004), 443-450
##[17]
S. Liao, The proposed homotopy analysis techniques for the solution of nonlinear problems, Ph.D. Dissertation. Shanghai Jiao Tong University, Shanghai (in English) (1992)
##[18]
S. Liao, Beyond perturbation: Introduction to the homotopy analysis method, CRC Press, Chapman and Hall, Boca Raton (2003)
##[19]
S. Liao, Notes on the homotopy analysis method: Some definitions and theorems, Commun. Nonlinear Sci. Numer. Simul., 14 (2009), 983-997
##[20]
Y. Liu Y, H. Shi, Existence of unbounded positive solutions for BVPs of singular fractional differential equations, J. Nonlinear Sci. Appl., 5 (2012), 281-293
##[21]
S. Momani, Z. Odibat, Homotopy perturbation method for nonlinear partial differential equations of fractional order, Phys. Lett. A., 365 (2007), 345-350
##[22]
S. Momani, Z. Odibat, Numerical comparison of methods for solving linear differential equations of fractional order, Chaos Solitons Fractals, 31 (2007), 1248-1255
##[23]
M. Inc, On exact solution of Laplace equation with Dirichlet and Neumann boundary conditions by the homotopy analysis method, Phys. Lett. A., 365 (2007), 412-415
##[24]
Z. Odibat, S. Momani, Modified homotopy perturbation method: application to quadratic Riccati differential equation of fractional order, Chaos Solitons Fractals, 36 (2008), 167-174
##[25]
Z. Odibat, S. Momani, Application of variational iteration method to nonlinear differential equation of fractional order , Int. J. Nonlinear Sci. Numer. Simul., 7 (2006), 27-34
##[26]
I. Podlubny, Fractional differential equations, Academic Press, New York (1999)
##[27]
T. Qiu, Z. Bai , Positive solutions for boundary value problem of nonlinear fractional differential equation, J. Nonlinear Sci. Appl., 1 (2008), 123-131
##[28]
M. Sajid, T. Javed, T. Hayat, MHD rotating flow of a viscous fluid over a shrinking surface, Nonlinear Dyn., 51 (2008), 259-265
##[29]
N. T. Shawagfeh, Analytical approximate solutions for nonlinear fractional differential equations, Appl. Math. Comput., 131 (2002), 517-529
##[30]
T. Wang, F. Xie, Existence and uniqueness of fractional differential equations with integral boundary conditions, J. Nonlinear Sci. Appl., 1 (2008), 206-212
##[31]
Y. Wang, Y. Yang, Positive solutions for Caputo fractional differential equations involving integral boundary conditions, J. Nonlinear Sci. Appl., 8 (2015), 99-109
##[32]
J. Wanga, X. Xionga, Y. Zhang, Extending synchronization scheme to chaotic fractional-order Chen systems, Physica A, 370 (2006), 279-285
##[33]
W. Yang, Positive solutions for singular coupled integral boundary value problems of nonlinear Hadamard fractional differential equations, J. Nonlinear Sci. Appl., 8 (2015), 110-129
##[34]
T. S. Zhou, C. Li, Synchronization in fractional-order differential systems, Phys. D., 212 (2005), 111-125
##[35]
H. Zhu, S. Zhou, Z. He, Chaos synchronization of the fractional-order Chen’s system, Chaos Solitons Fractals, 41 (2009), 2733-2740
]
Strong convergence of a Halpern-type iteration algorithm for fixed point problems in Banach spaces
Strong convergence of a Halpern-type iteration algorithm for fixed point problems in Banach spaces
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en
In this paper, we studied a Halpern-type iteration algorithm involving pseudo-contractive mappings for
solving some variational inequality in a q-uniformly smooth Banach space. We show the studied algorithm
has strong convergence under some mild conditions. Our result extends and improves many results in the
literature.
489
495
Zhangsong
Yao
School of Information Engineering
Nanjing Xiaozhuang University
China
yaozhsong@163.com
Li-Jun
Zhu
School of Mathematics and Information Science
Beifang University of Nationalities
China
zhulijun1995@sohu.com
Yeong-Cheng
Liou
Department of Information Management
Center for General Education
Cheng Shiu University
Kaohsiung Medical University
Taiwan
Taiwan
simplex_liou@hotmail.com
Halpern iterative algorithm
pseudocontractive mapping
fixed point
variational inequality
Article.4.pdf
[
[1]
F. E. Browder, W. V. Petryshyn, Construction of fixed points of nonlinear mappings in Hilbert spaces, J. Math. Anal. Appl., 20 (1967), 197-228
##[2]
C. O. Chidume, G. De Souza , Convergence of a Halpern-type iteration algorithm for a class of pseudocontractive mappings, Nonliear Anal., 69 (2008), 2286-2292
##[3]
P. Li, S. M. Kang, L. Zhu, Visco-resolvent algorithms for monotone operators and nonexpansive mappings, J. Nonlinear Sci. Appl., 7 (2014), 325-344
##[4]
G. Marino, H. K. Xu, Weak and strong convergence theorems for strictly pseudocontractions in Hilbert spaces, J. Math. Anal. Appl., 329 (2007), 336-346
##[5]
C. H. Morales, J. S. Jung, Convergence of paths for pseudocontractive mappings in Banach spaces, Proc. Amer. Math. Soc., 128 (2000), 3411-3419
##[6]
M. A. Noor, General variational inequalities, Appl. Math. Lett., 1 (1988), 119-121
##[7]
M. A. Noor, Some developments in general variational inequalities, Appl. Math. Comput., 152 (2004), 199-277
##[8]
M. A. Noor, Differentiable nonconvex functions and general variational inequalities, Appl. Math. Comput., 199 (2008), 623-630
##[9]
M. A. Noor, K. I. Noor, Self-adaptive projection algorithms for general variational inequalities, Appl. Math. Comput., 151 (2004), 659-670
##[10]
M. A. Noor, K. I. Noor, Th. M. Rassias, Some aspects of variational inequalities, J. Comput. Appl. Math., 47 (1993), 285-312
##[11]
M. O. Osilike, A. Udomene, Demiclosedness principle and convergence theorems for strictly pseudocontractive mappings of Browder-Petryshyn Type, J. Math. Anal. Appl., 256 (2001), 431-445
##[12]
P. Shi, Equivalence of variational inequalities with Wiener-Hopf equations, Proc. Amer. Math. Soc., 111 (1991), 339-346
##[13]
G. Stampacchia, Formes bilineaires coercitives sur les ensembles convexes, C.R. Acad. Sci. Paris, 258 (1964), 4413-4416
##[14]
T. Suzuki, Strong convergence theorems for infinite families of nonexpansive mappings in general Banach spaces, Fixed Point Theory Appl., 2005 (2005), 103-123
##[15]
H. K. Xu, Inequalities in Banach spaces with applications , Nonlinear Anal., 16 (1991), 1127-1138
##[16]
H. K. Xu, Viscosity approximation methods for non-expansive mappings, J. Math. Anal. Appl., 298 (2004), 279-291
##[17]
J. C. Yao, Variational inequalities with generalized monotone operators, Math. Operations Research, 19 (1994), 691-705
##[18]
Y. Yao, Y. J. Cho, Y. C. Liou, R. P. Agarwal, Constructed nets with perturbations for equilibrium and fixed point problems, J. Inequal. Appl., 2014 (2014), 1-14
##[19]
Y. Yao, Y. C. Liou, C. C. Chyu , Fixed points of pseudocontractive mappings by a projection method in Hilbert spaces, J. Nonlinear Convex Anal., 14 (2013), 785-794
##[20]
Y. Yao, Y. C. Liou, S. M. Kang , Coupling extragradient methods with CQ mathods for equilibrium points, pseudomontone variational inequalities and fixed points, Fixed Point Theory, 15 (2014), 311-324
##[21]
Y. Yao, M. Postolache, S. M. Kang, Strong convergence of approximated iterations for asymptotically pseudocontractive mappings, Fixed Point Theory Appl., 2014 (2014), 1-13
##[22]
H. Y. Zhou , Convergence theorems of fixed points for k-strict pseudocontractions in Hilbert spaces, Nonlinear Anal., 69 (2008), 456-462
]
Binary Bargmann symmetry constraint associated with \(3\times 3\) discrete matrix spectral problem
Binary Bargmann symmetry constraint associated with \(3\times 3\) discrete matrix spectral problem
en
en
Based on the nonlinearization technique, a binary Bargmann symmetry constraint associated with a new
discrete \(3\times 3\) matrix eigenvalue problem, which implies that there exist infinitely many common commuting
symmetries and infinitely many common commuting conserved functionals, is proposed. A new symplectic
map of the Bargmann type is obtained through binary nonlinearization of the discrete eigenvalue problem
and its adjoint one. The generating function of integrals of motion is obtained, by which the symplectic
map is further proved to be completely integrable in the Liouville sense.
496
506
Xin-Yue
Li
College of Mathematics and Systems Science
Shandong University of Science and Technology
P. R. China
xinyueliqd@sina.com
Qiu-Lan
Zhao
College of Mathematics and Systems Science
Shandong University of Science and Technology
P. R. China
ql_zhao@aliyun.com
Yu-Xia
Li
Shandong Key Laboratory for Robot and Intelligent Technology
P. R. China
Huan-He
Dong
College of Mathematics and Systems Science
Shandong University of Science and Technology
P. R. China
Discrete Hamiltonian structure
binary Bargmann symmetry constraint
finite-dimensional integrable system .
Article.5.pdf
[
[1]
M. Antonowicz, S. Wojciechowski , How to construct finite-dimensional bi-Hamiltonian systems from soliton equations: Jacobi integrable potentials, J. Math. Phys., 33 (1992), 2115-2125
##[2]
M. Blaszak, K. Marciniak , R-matrix approach to lattice integrable systems, J. Math. Phys., 35 (1994), 4661-4682
##[3]
C. W. Cao, Nonlinearization of the Lax system for AKNS hierarchy, Sci. China Ser. A, 33 (1990), 528-536
##[4]
H. H. Dong, J. Su, F. J. Yi, T. Q. Zhang, New Lax pairs of the Toda lattice and the nonlinearization under a higher-order Bargmann constraint, J. Math. Phys., 53 (2012), 1-18
##[5]
A. S. Fokas, R. L. Anderson, On the use of isospectral eigenvalue problems for obtaining hereditary symmetries for Hamiltonian systems, J. Math. Phys., 23 (1982), 1066-1073
##[6]
E. G. Fan, Y. C. Hon , Super extension of Bell polynomials with applications to supersymmetric equations, J. Math. Phys., 53 (2012), 13503-13520
##[7]
X. G. Geng, Finite-dimensional discrete systems and integrable systems through nonlinearization of the discrete eigenvalue problem, J. Math. Phys., 34 (1993), 805-817
##[8]
X. B. Hu, D. L. Wang, Hon-Wah Tan, Lax pairs and Bäcklund transformations for a coupled Ramani equation and its related system, Appl. Math. Lett., 13 (2000), 45-48
##[9]
Y. S. Li, W. X. Ma, Binary nonlinearization of AKNS spectral problem under higher-order symmetry constraints, Chaos Solitons Fractals, 11 (2000), 697-710
##[10]
X. Y. Li, X. J. Li, Y. X. Li, The Liouville integrable lattice equations associated with a discrete three-by-three matrix spectral problem, Internat. J. Modern Phys. B, 25 (2011), 1251-1261
##[11]
X. Y. Li, Q. L. Zhao, Y. X. Li, A new integrable symplectic map for 4-field Blaszak-Marciniak lattice equations, Commun. Nonlinear Sci. Numer. Simul., 19 (2014), 2324-2333
##[12]
W. X. Ma , Symmetry constraint of MKdV equations by binary nonlinearization, Physica A, 219 (1995), 467-481
##[13]
W. X. Ma, X. G. Geng, Bäcklund transformations of soliton systems from symmetry constraints, CRM Proc. Lecture Notes, 29 (2001), 313-323
##[14]
W. X. Ma, W. Strampp , An explicit symmetry constraint for the Lax pairs and the adjoint Lax pairs of AKNS systems , Phys. Lett. A, 185 (1994), 277-286
##[15]
W. X. Ma, B. Fuchssteiner, W. Oevel , A three-by-three matrix spectral problem for AKNS hierarchy and its binary nonlinearization, Physica A, 233 (1996), 331-354
##[16]
W. X. Ma , Binary Bargmann symmetry constraints of soliton equations, Nonlinear Anal., 47 (2001), 5199-5211
##[17]
W. X. Ma, R. G. Zhou , Binary nonlinearization of spectral problems of the perturbation AKNS systems , Chaos Solitons Fractals, 13 (2002), 1451-1463
##[18]
W. X. Ma, Z. X. Zhou, Binary symmetry constraints of N-wave interaction equations in 1+1 and 2+1 dimensions , J. Math. Phys., 42 (2001), 4345-4382
##[19]
W. X. Ma, A. Abdeljabbar, A bilinear Bäcklund transformation of a (3+1)-dimensional generalized KP equation, Appl. Math. Lett., 25 (2012), 1500-1504
##[20]
W. X. Ma, Bilinear equations and resonant solutions characterized by Bell polynomials, Rep. Math. Phys., 72 (2013), 41-56
##[21]
W. X. Ma, Y. Zhang, Y. N. Tang, J. Y. Tu, Hirota bilinear equations with linear subspaces of solutions, Appl. Math. Comput., 218 (2012), 7174-7183
##[22]
Z. J. Qiao, Integrable Hierarchy, \(3\times 3\) Constrained Systems, and Parametric Solutions, Acta Appl. Math., 83 (2004), 199-220
##[23]
Y. T. Wu, X. G. Geng, A new integrable symplectic map associated with lattice equations, J. Math. Phys., 37 (1996), 2338-2345
##[24]
X. X. Xu, Factorization of a hierarchy of the lattice soliton equations from a binary Bargmann symmetry constraint, Nonlinear Anal., 61 (2005), 1225-1233
##[25]
Y. Xu, R. G. Zhou, Integrable decompositions of a symmetric matrix Kaup-Newell equation and a symmetric matrix derivative nonlinear Schrödinger equation, Appl. Math. Comput., 219 (2013), 4551-4559
##[26]
R. G. Zhou , Integrable Rosochatius deformations of the restricted soliton flows, J. Math. Phys., 48 (2007), 1-17
##[27]
Y. Zhang, Positons, negatons and complexitons of the mKdV equation with non-uniformity terms, Appl. Math. Comput., 217 (2010), 1463-1469
##[28]
Y. F. Zhang, Z. Han, Hon-Wah Tam, An integrable hierarchy and Darboux transformations, bilinear Bäcklund transformations of a reduced equation, Appl. Math. Comput., 219 (2013), 5837-5848
##[29]
Z. N. Zhu, Z. M. Zhu, X. N. Wu, W. M. Xue , New Matrix Lax Representation for a Blaszak-Marciniak Four-Field Lattice Hierarchy and Its Infinitely Many Conservation Laws, J. Phys. Soc. Japan, 71 (2002), 1864-1869
##[30]
Y. B. Zeng, X. Cao , Separation of variables for higher-order binary constrained flows of the Tu hierarchy , Adv. Math. (China), 31 (2002), 135-147
##[31]
Q. L. Zhao, Y. X. Li, X. Y. Li, Y. P. Sun, The finite-dimensional super integrable system of a super NLS-mKdV equation, Commun. Nonlinear Sci. Numer. Simul., 17 (2012), 4044-4052
##[32]
Q. L. Zhao, Y. X. Li , The binary nonlinearization of generalized Toda hierarchy by a special choice of parameters, Commun. Nonlinear Sci. Numer. Simul., 16 (2011), 3257-3268
##[33]
Q. L. Zhao, X. Y. Li, F. S. Liu , Two integrable lattice hierarchies and their respective Darboux transformations, Appl. Math. Comput., 219 (2013), 5693-5705
##[34]
Q. L. Zhao, X. Z. Wang, The integrable coupling system of a \(3 \times 3\) discrete matrix spectral problem, Appl. Math. Comput., 216 (2010), 730-743
]
Dynamics of a Harvested Logistic Type Model with Delay and Piecewise Constant Argument
Dynamics of a Harvested Logistic Type Model with Delay and Piecewise Constant Argument
en
en
In this paper, a harvested logistic equation with delay and piecewise constant argument of generalized type
is addressed. Both discrete and piecewise constant delays are incorporated into the logistic equation for
investigation. Existence, boundedness of positive solutions and permanence are studied for the proposed
logistic model.
507
517
Duygu
Aruğaslan
Department of Mathematics
Süleyman Demirel University
Turkey
duyguarugaslan@sdu.edu.tr
Delayed logistic equation
piecewise constant argument of generalized type
boundedness
permanence
harvesting.
Article.6.pdf
[
[1]
M. U. Akhmet, Integral manifolds of differential equations with piecewise constant argument of generalized type, Nonlinear Anal., 66 (2007), 367-383
##[2]
M. U. Akhmet, On the reduction principle for differential equations with piecewise constant argument of generalized type, J. Math. Anal. Appl., 336 (2007), 646-663
##[3]
M. U. Akhmet , Stability of differential equations with piecewise constant arguments of generalized type, Nonlinear Anal., 68 (2008), 794-803
##[4]
M. U. Akhmet, D. Aruğaslan, X. Liu, Permanence of nonautonomous ratio-dependent predator-prey systems with piecewise constant argument of generalized type, Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal., 15 (2008), 37-51
##[5]
M. U. Akhmet, Asymptotic behavior of solutions of differential equations with piecewise constant arguments, Appl. Math. Lett., 21 (2008), 951-956
##[6]
M. U. Akhmet, D. Aruğaslan, Lyapunov-Razumikhin method for differential equations with piecewise constant argument , Discrete Contin. Dyn. Syst., 25 (2009), 457-466
##[7]
M. U. Akhmet, D. Aruğaslan, E. Yılmaz, Stability in cellular neural networks with a piecewise constant argument, J. Comput. Appl. Math., 233 (2010), 2365-2373
##[8]
M. U. Akhmet, D. Aruğaslan, E. Yılmaz, Method of Lyapunov functions for differential equations with piecewise constant delay, J. Comput. Appl. Math., 235 (2011), 4554-4560
##[9]
M. Akhmet, Nonlinear Hybrid Continuous/Discrete-Time Models , Atlantis Press, Paris (2011)
##[10]
M. Akhmet , Almost periodic solutions of second order neutral functional differential equations with piecewise constant argument, Discontin. Nonlinearity Complex, 2 (2013), 369-388
##[11]
M. U. Akhmet, Quasilinear retarded differential equations with functional dependence on piecewise constant argument, Commun. Pure Appl. Anal., 13 (2014), 929-947
##[12]
O. Binda, M. Pierre, Asymptotic expansion for a delay differential equation with continuous and piecewise constant arguments, Funkcial. Ekvac, 50 (2007), 421-448
##[13]
K. L. Cooke, J. Wiener, Retarded differential equations with piecewise constant delays, J. Math. Anal. Appl., 99 (1984), 265-297
##[14]
J. Cui, H.-Xu. Li , Delay differential logistic equation with linear harvesting, Nonlinear Anal. Real World Appl., 8 (2007), 1551-1560
##[15]
J. Dhar, A. K. Sharma, S. Tegar, The role of delay in digestion of plankton by fish population: a fishery model, J. Nonlinear Sci. Appl., 1 (2008), 13-19
##[16]
R. Levins , Some demographic and genetic consequences of environmental heterogeneity for biological control , Bull. Entomology Soc. America, 15 (1969), 237-240
##[17]
H. Matsunaga, T. Hara, S. Sakata, Global attractivity for a logistic equation with piecewise constant argument, Nonlinear Differential Equations Appl., 8 (2001), 45-52
##[18]
Y. Muroya , Permanence, contractivity and global stability in logistic equations with general delays, J. Math. Anal. Appl., 302 (2005), 389-401
##[19]
G. Seifert, Second-order neutral delay-differential equations with piecewise constant time dependence, J. Math. Anal. Appl., 281 (2003), 1-9
##[20]
Z. Wang, J. Wu, The stability in a logistic equation with piecewise constant arguments, Differential Equations Dynam. Systems, 14 (2006), 179-193
##[21]
J. Wiener, V. Lakshmikantham, A damped oscillator with piecewise constant time delay , Nonlinear Stud., 7 (2000), 78-84
##[22]
X. Yang, Existence and exponential stability of almost periodic solution for cellular neural networks with piecewise constant argument, Acta Math. Appl. Sin., 29 (2006), 789-800
]
Fixed point theorems for \(\alpha-\beta-\psi\)-contractive mappings in partially ordered sets
Fixed point theorems for \(\alpha-\beta-\psi\)-contractive mappings in partially ordered sets
en
en
In this paper, we introduce a new concept of \(\alpha-\beta-\psi\)-contractive type mappings and construct some fixed
point theorems for such mappings in metric spaces endowed with partial order. Moreover, we use fixed
point theorems to find a solution for the first-order boundary value differential equation.
518
528
Mohammad Sadegh
Asgari
Department of Mathematics, Faculty of Science
Central Tehran Branch, Islamic Azad University
Iran
moh.asgari@iauctb.ac.ir;msasgari@yahoo.com
Ziad
Badehian
Department of Mathematics, Faculty of Science
Central Tehran Branch, Islamic Azad University
Iran
ziadbadehian@gmail.com;zia.badehian.sci@iauctb.ac.ir
Fixed point
\(\alpha-\beta-\psi\)-contractive mappings
partially ordered sets
lower and upper solutions.
Article.7.pdf
[
[1]
R. P. Agarwal, M. A. El-Gebeily, D. O'Regan, Generalized contractions in partially ordered metric spaces , Appl. Anal., 87 (2008), 109-116
##[2]
I. Altun, H. Simsek , Some fixed point theorems on ordered metric spaces and application, Fixed Point Theory Appl., 2010 (2010), 1-17
##[3]
I. Beg, A. R. Butt, Fixed point for set-valued mappings satisfying an implicit relation in partially ordered metric spaces, Nonlinear Anal., 71 (2009), 3699-3704
##[4]
V. Berinde, F. Vetro, Common fixed points of mappings satisfying implicit contractive conditions, Fixed Point Theory Appl., 2012 (2012), 1-8
##[5]
Lj. Ćirić, N. Cakić, M. Rajović, J. Ume , Monotone Generalized Nonlinear Contractions in Partially Ordered Metric Spaces, Fixed Point Theory Appl., 2008 (2008), 1-11
##[6]
M. Cosentino, P. Salimi, P. Vetro, Fixed point results on metric-type spaces, Acta Math. Sci. Ser. B Engl. Ed., 34 (2014), 1237-1253
##[7]
J. Harjani, K. Sadarangani , Fixed point theorems for weakly contractive mappings in partially ordered sets, Non- linear Anal., 71 (2009), 3403-3410
##[8]
J. Harjani, K. Sadarangani, Generalized contractions in partially ordered metric spaces and applications to ordinary differential equations, Nonlinear Anal., 72 (2010), 1188-1197
##[9]
P. Kumam, C. Vetro, F. Vetro, Fixed points for weak \(\alpha-\psi\)-contractions in partial metric spaces, Abstr. Appl. Anal., 2013 (2013), 1-9
##[10]
G. Ladde, V. Lakshmikantham, A. Vatsala , Monotone iterative techniques for nonlinear differential equations, Monographs, Advanced Texts and Surveys in Pure and Applied Mathematics, Pitman (Advanced Publishing Program), Boston (1985)
##[11]
H. K. Nashine, B. Samet, Fixed point results for mappings satisfying \(\alpha-\psi\)-weakly contractive condition in partially ordered metric spaces, Nonlinear Anal., 74 (2011), 2201-2209
##[12]
J. J. Nieto, R. L. Pouso, R. Rodríguez-López, Fixed point theorems in ordered abstract spaces, Proc. Amer. Math. Soc., 137 (2007), 2505-2517
##[13]
J. J. Nieto, R. Rodríguez-López , Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order, 22 (2005), 223-239
##[14]
J. J. Nieto, R. Rodríguez-López, Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations, Acta Math. Sin. (Engl. Ser.), 23 (2007), 2205-2212
##[15]
D. O'Regan, A. Petruşel, Fixed point theorems for generalized contractions in ordered metric spaces, J. Math. Anal. Appl., 341 (2008), 1241-1252
##[16]
D. Paesano, P. Vetro, Common fixed Points in a partially ordered partial metric space, Int. J. Anal., 2013 (2013), 1-8
##[17]
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 (2003), 1435-1443
##[18]
B. Samet, C. Vetro, P. Vetro, Fixed point theorems for \(\alpha-\psi\)-contractive type mappings, Nonlinear Anal., 75 (2012), 2154-2165
##[19]
D. Turkoglu, D. Binbasioglu, Some Fixed-Point Theorems for Multivalued Monotone Mappings in Ordered Uniform Space, Fixed Point Theory Appl., 2011 (2011), 1-12
##[20]
E. Zeidler, Nonlinear functional analysis and its applications, Vol. I, Springer, New York (1986)
]
Some generalized fixed point theorems in the context of ordered metric spaces
Some generalized fixed point theorems in the context of ordered metric spaces
en
en
In this paper, we give three main theorems which are new generalizations of Banach fixed point theorem,
Kannan fixed point theorem and Chatterjea fixed point theorem in the context of the ordered metric space.
529
539
Mehmet
Kir
Department of Mathematics, Faculty of Science
Ataturk University
Turkey
mehmetkir04@gmail.com
Hukmi
Kiziltunc
Department of Mathematics, Faculty of Science
Ataturk University
Turkey
hukmu@atauni.edu.tr
Fixed point
Chatterjea fixed point theorem
Kannan fixed point theorem
contraction mappings.
Article.8.pdf
[
[1]
S. Banach , Sur les operations dans les ensembles abstraits et leur application aux equations integerales, Fund. Math., 3 (1922), 133-181
##[2]
A. Branciari , A fixed point theorem for mapping satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci., 29 (2002), 531-536
##[3]
S. K. Chatterjea , Fixed point theorems, C.R. Acad. Bulgare Sci., 25 (1972), 727-730
##[4]
R. Kannan, Some results on fixed points, Bull. Cal. Math. Soc., 60 (1968), 71-76
##[5]
M. Kır, H. Kızıltuc, \(T_F\)-contractive conditions for Kannan and Chatterjea fixed point theorems, Adv. Fixed Point Theory, 4 (2014), 140-148
##[6]
N. Malhotra, B. Bansal , Some common coupled fixed point theorems for generalized contraction in b-metric spaces, J. Nonlinear Sci. Appl., 8 (2015), 8-16
##[7]
Z. Mustafa, J. R. Roshan, V. Parvaneh, Z. Kadelburg, Fixed point theorems for weakly T-Chatterjea and weakly T-Kannan contractions in b-metric spaces, J. Inequal. Appl., 2014 (2014), 1-14
##[8]
S. Moradi, A. Davood, New extension of Kannan fixed point theorem on complete metric and generalized metric spaces , Int. J. Math. Anal., 5 (2011), 2313-2320
##[9]
S. Moradi, A. Beiranvand, Fixed point of \(T_F\)-contractive single-valued mappings, Iran. J. Math. Sci. Inform., 5 (2010), 25-32
##[10]
J. J. Nieto, R. Rodríguez-López , Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order , 22 (2005), 223-239
##[11]
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
]
The uniform boundedness principles for \(\gamma\)-max-pseudo-norm-subadditive and quasi-homogeneous operators in \(F^*\) spaces
The uniform boundedness principles for \(\gamma\)-max-pseudo-norm-subadditive and quasi-homogeneous operators in \(F^*\) spaces
en
en
In this paper, we prove that every \(F^*\) space (i.e., Hausdorff topological vector space satisfying the first
countable axiom) can be characterized by means of its “standard generating family of pseudo-norms”. By
using the standard generating family of pseudo-norms \(\mathcal{P}\), the concepts of \(\mathcal{P}\)-bounded set and \(\gamma\)-maxpseudo-
norm-subadditive operator in \(F^*\) space are introduced. The uniform boundedness principles for
family of \(\gamma\)-max-pseudo-norm-subadditive and quasi-homogeneous operators in \(F^*\) spaces are established.
As applications, we obtain the corresponding uniform boundedness principles in classical normed spaces and
Menger probabilistic normed spaces.
540
556
Ming-liang
Song
Mathematics and Information Technology School
Jiangsu Second Normal University
P. R. China
mlsong2004@163.com
Uniform boundedness principle
\(\gamma\)-max-pseudo-norm-subadditive operator
quasi-homogeneous operator
second category
\(F^*\) space.
Article.9.pdf
[
[1]
C. Alegre, S. Romaguera, P. Veeramani , The uniform boundedness theorem in asymmetric normed spaces , Abstr. Appl. Anal., 2012 (2012), 1-8
##[2]
S. Banach , Theorie des operations lineaires, Warszawa, (1932)
##[3]
S. S. Chang, Y. J. Cho, S. M. Kang, Nonlinear operator theory in probabilistic metric spaces, Nova Science Publishers Inc., New York (2001)
##[4]
A. H. Chen, R. L. Li, A version of Orlicz-Pettis theorem for quasi-homogeneous operator space, J. Math. Anal. Appl., 373 (2011), 127-133
##[5]
G. G. Ding , The uniform boundedness principle in some topological vector groups , J. Syst. Sci. Complex, 13 (2000), 292-301
##[6]
H. Ishihara , The uniform boundedness theorem and a boundedness principle, Ann. Pure Appl. Logic, 163 (2012), 1057-1061
##[7]
R. L. Li, M. K. Shin, C. Swartz, Operator matrices on topological vector spaces, J. Math. Anal. Appl., 274 (2002), 645-658
##[8]
O. Nygaard, A strong uniform boundedness principle in Banach spaces, Proc. Amer. Math. Soc., 129 (2001), 861-863
##[9]
J. H. Qiu, Resonance theorems for families of quasi-homogeneous operators, Chinese Ann. Math. Ser. A, 25 (2004), 389-396
##[10]
W. Roth, A uniform boundedness theorem for locally convex cones, Proc. Amer. Math. Soc. , 126 (1998), 1973-1982
##[11]
M. L. Song, Resonance theorems for family of pointwise semi-bounded and non-unbounded linear operators on \(F^*\) spaces, Acta Math. Sci. Ser. A., 34 (2014), 1071-1082
##[12]
M. L. Song, J. X. Fang, Resonance theorems for family of quasi-homogeneous operators in fuzzy normed linear spaces, Fuzzy Sets and Systems, 159 (2008), 708-719
##[13]
B. Schweizer, A. Sklar, Probabilistic metric space, North-Holland Publishing Co., New York (1983)
##[14]
J. L. Shou, M. S. Wang, Introduction to analytic topology, Xian: Xian Jiaotong University Press, in Chinese (1988)
##[15]
L. Vesely, Local uniform boundedness principle for families of ϵ-monotone operators, Nonlinear Anal.-TMA, 24 (1995), 1299-1304
##[16]
A. Wilansky, Modern Methods in Topological Vector Spaces, Blaisdel, New York (1978)
##[17]
J. Z. Xiao, X. H. Zhu, Probabilistic norm of operators and resonance theorems, Appl. Math. Mech., 20 (1999), 781-788
##[18]
S. H. Zhang, R. L. Li , Uniform boundedness principle for ordered topological vector spaces , Ann. Funct. Anal., 2 (2011), 13-18
]
Existence of an optimal control for fractional stochastic partial neutral integro-differential equations with infinite delay
Existence of an optimal control for fractional stochastic partial neutral integro-differential equations with infinite delay
en
en
In this paper we study optimal control problems governed by fractional stochastic partial neutral functional
integro-differential equations with infinite delay in Hilbert spaces. We prove an existence result of mild
solutions by using the fractional calculus, stochastic analysis theory, and fixed point theorems with the
properties of analytic α-resolvent operators. Next, we derive the existence conditions of optimal pairs of
these systems. Finally an example of a nonlinear fractional stochastic parabolic optimal control system is
worked out in detail.
557
577
Zuomao
Yan
School of Mathematics and Statistics
Lanzhou University
P. R. China
yanzuomao@163.com
Fangxia
Lu
Department of Mathematics,
Hexi University
P. R. China
zhylfx@163.com
Fractional stochastic partial neutral functional integro-differential equations
optimal controls
infinite delay
analytic α-resolvent operator
fixed point theorem.
Article.10.pdf
[
[1]
O. P. Agrawal , A general formulation and solution scheme for fractional optimal control problems, Nonlinear Dynam., 38 (2004), 323-337
##[2]
R. P. Agarwal, J. P. C. Santos, C. Cuevas, Analytic resolvent operator and existence results for fractional order evolutionary integral equations, J. Abstr. Differ. Equ. Appl., 2 (2012), 26-47
##[3]
N. U. Ahmed , Existence of optimal controls for a general class of impulsive systems on Banach spaces, SIAM J. Control Optim., 42 (2003), 669-685
##[4]
N. U. Ahmed, Relatively optimal filtering on a Hilbert space for measure driven stochastic systems, Nonlinear Anal., 72 (2010), 3695-3706
##[5]
N. U. Ahmed, Existence of optimal output feedback control law for a class of uncertain infinite dimensional stochastic systems: a direct approach, Evol. Equ. Control Theory, 1 (2012), 235-250
##[6]
N. U. Ahmed, Stochastic neutral evolution equations on Hilbert spaces with partially observed relaxed control and their necessary conditions of optimality, Nonlinear Anal., 101 (2014), 66-79
##[7]
J-M. Bismut, On optimal control of linear stochastic equations with a linear-quadratic criterion, SIAM J. Control Optim., 15 (1977), 1-4
##[8]
Z. Brzeźniak, R. Serrano , Optimal relaxed control of dissipative stochastic partial differential equations in Banach spaces, SIAM J. Control Optim., 51 (2013), 2664-2703
##[9]
G. Da Prato, J. Zabczyk , Stochastic Equations in Infinite Dimensions, Cambridge University Press, Cambridge (1992)
##[10]
B. de Andrade, J. P. C. Santos , Existence of solutions for a fractional neutral integro-differential equation with unbounded delay, Electron. J. Differential Equations, 2012 (2012), 1-13
##[11]
M. M. El-Borai, Some probability densities and fundamental solutions of fractional evolution equations, Chaos Solitons Fractals, 14 (2002), 433-440
##[12]
M. M. El-Borai, K. E-S. EI-Nadi, H. A. Fouad , On some fractional stochastic delay differential equations, Comput. Math. Appl., 59 (2010), 1165-1170
##[13]
J. K. Hale, J. Kato, Phase spaces for retarded equations with infinite delay, Funkcial. Ekvac., 21 (1978), 11-41
##[14]
Y. Hino, S. Murakami, T. Naito, Functional-Differential Equations with Infinite Delay, Lecture Notes in Mathematics, Springer-Verlag, Berlin (1991)
##[15]
C. M. Marle, Measures et Probabilités, Hermann, Paris, France (1974)
##[16]
Q. Meng, P. Shi, Stochastic optimal control for backward stochastic partial differential systems, J. Math. Anal. Appl., 402 (2013), 758-771
##[17]
G. M. Mophou, Optimal control of fractional diffusion equation, Comput. Math. Appl., 61 (2011), 68-78
##[18]
B. Øksendal, A. Sulem, Applied Stochastic Control of Jump Diffusions, Springer-Verlag, Berlin (2007)
##[19]
A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, New York (1983)
##[20]
I. Podlubny , Fractional Differential Equations, Mathematics in Sciences and Engineering, Academic Press, San Diego (1999)
##[21]
B. N. Sadovskii, On a fixed point principle, Funct. Anal. Appl., 1 (1967), 151-153
##[22]
R. Sakthivel, R. Ganesh, S. Suganya, Approximate controllability of fractional neutral stochastic system with infinite delay, Rep. Math. Phys., 70 (2012), 291-311
##[23]
C. Tudor , Optimal control for semilinear stochastic evolution equations, Appl. Math. Optim., 20 (1989), 319-331
##[24]
J. Wang, Y. Zhou, M. Medved, On the solvability and optimal controls of fractional integrodifferential evolution systems with infinite delay, J. Optim. Theory Appl., 152 (2012), 31-50
##[25]
J. Wang, Y. Zhou, W. Wei, H. Xu, Nonlocal problems for fractional integrodifferential equations via fractional operators and optimal controls, Comput. Math. Appl., 62 (2011), 1427-1441
##[26]
Z. Yan, H. Zhang, Asymptotic stability of fractional impulsive neutral stochastic partial integro-differential equations with state-dependent delay, Electron. J. Differential Equations, 2013 (2013), 1-29
##[27]
J. Zhou, B. Liu, Optimal control problem for stochastic evolution equations in Hilbert spaces, Internat. J. Control, 83 (2010), 1771-1784
##[28]
X. Zhu, J. Zhou , Infinite horizon optimal control of stochastic delay evolution equations in Hilbert spaces, Abstr. Appl. Anal., 2013 (2013), 1-14
]
Global stability of a time-delayed multi-group SIS epidemic model with nonlinear incidence rates and patch structure
Global stability of a time-delayed multi-group SIS epidemic model with nonlinear incidence rates and patch structure
en
en
In this paper, we formulate and study a multi-group SIS epidemic model with time-delays, nonlinear incidence
rates and patch structure. Two types of delays are incorporated to concern the time-delay of infection
and that for population exchange among different groups. Taking into account both of the effects of crossregion
infection and the population exchange, we define the basic reproduction number \(\mathcal{R}_0\) by the spectral
radius of the next generation matrix and prove that it is a threshold value, which determines the global
stability of each equilibrium of the model. That is, it is shown that if \(\mathcal{R}_0\leq 1\), the disease-free equilibrium
is globally asymptotically stable, while if \(\mathcal{R}_0 > 1\), the system is permanent, an endemic equilibrium exists
and it is globally asymptotically stable. These global stability results are achieved by constructing Lyapunov
functionals and applying LaSalle's invariance principle to a reduced system. Numerical simulation is
performed to support our theoretical results.
578
599
Jinliang
Wang
School of Mathematical Science
Heilongjiang University
China
jinliangwang@hlju.edu.cn
Yoshiaki
Muroya
Department of Mathematics
Waseda University 3-4-1 Ohkubo
Japan
ymuroya@waseda.jp
Toshikazu
Kuniya
Graduate School of System Informatics
Kobe University
Japan
tkuniya@port.kobe-u.ac.jp
SIS epidemic model
time-delay
nonlinear incidence rate
patch structure.
Article.11.pdf
[
[1]
J. Arino, P. V. D. Driessche, A multi-city epidemic model , Math. Popul. Stud., 10 (2003), 175-193
##[2]
F. V. Atkinson, J. R. Haddock, On determining phase spaces for functional differential equations, Funkcial. Ekvac., 31 (1988), 331-347
##[3]
E. Beretta, Y. Takeuchi, Global stability of an SIR epidemic model with time delays, J. Math. Biol., 33 (1995), 250-260
##[4]
A. Berman, R. Plemmons, Nonnegative Matrices in the Mathematical Sciences, Academic Press, New York- London (1979)
##[5]
F. Brauer, P. V. D. Driessche, Models for transmission of disease with immigration of infectives, Math. Biosci., 171 (2001), 143-154
##[6]
J. Cui, Y. Takeuchi, Z. Lin, Permanent and extinction for dispersal population systems, J. Math. Anal. Appl., 298 (2004), 73-93
##[7]
O. Diekmann, J. A. P. Heesterbeek, J. A. J. Metz, On the definition and the computation of the basic reproduction ratio \(R_0\) in models for infectious diseases in heterogeneous populations, J. Math. Biol., 28 (1990), 365-382
##[8]
Y. Enatsu, Y. Nakata, Y. Muroya, Global stability of SIR epidemic models with a wide class of nonlinear incidence rates and distributed delays, Discrete Contin. Dyn. Syst. B, 15 (2011), 61-74
##[9]
T. Faria, Global dynamics for Lotka-Volterra systems with infinite delay and patch structure, Appl. Math. Comput., 245 (2014), 575-590
##[10]
M. Fiedler, Special matrices and their applications in numerical mathematics, Martinus Nijhoff Publishers, Dordrecht (1986)
##[11]
H. Guo, M. Y. Li, Z. S. Shuai, Global stability of the endemic equilibrium of multigroup SIR epidemic models, Can. Appl. Math. Quart., 14 (2006), 259-284
##[12]
H. W. Hethcote, Qualitative analyses of communicable disease models, Math Biosci., 28 (1976), 335-356
##[13]
Y. Hino, S. Murakami, T. Naito, Functional Differential Equations with Infinite Delay, Springer, Berlin (1991)
##[14]
Y. Jin, W. Wang, The effect of population dispersal on the spread of a disease, J. Math. Anal. Appl., 308 (2005), 343-364
##[15]
W. O. Kermack, A. G. McKendrick, Contributions to the mathematical theory of epidemics I, Bull. Math. Bio., 53 (1991), 33-55
##[16]
T. Kuniya, Y. Muroya, Global stability of a multi-group SIS epidemic model for population migration, Disc. Cont. Dyn. Syst. B, 19 (2014), 1105-1118
##[17]
T. Kuniya, Y. Muroya, Global stability of a multi-group SIS epidemic model with varying total population size, Appl. Math. Comput., (accepted), -
##[18]
A. Lajmanovich, J. A. Yorke, A deterministic model for gonorrhea in a nonhomogeneous population, Math. Biosci., 28 (1976), 221-236
##[19]
J. P. LaSalle, The stability of dynamical systems, SIAM, Philadelphia (1976)
##[20]
S. Levin , Dispersion and population interactions, Amer. Nat., 108 (1974), 207-228
##[21]
M. Y. Li, Z. S. Shuai, Global stability of an epidemic model in a patchy environment, Can. Appl. Math. Q., 17 (2009), 175-187
##[22]
M. Y. Li, Z. S. Shuai, Global-stability problem for coupled systems of differential equations on networks, J. Diff. Equ., 284 (2010), 1-20
##[23]
Y. Muroya, Practical monotonous iterations for nonlinear equations, Mem. Fac. Sci. Kyushu Univ. A., 22 (1968), 56-73
##[24]
Y. Muroya, Y. Enatsu, T. Kuniya, Global stability of extended multi-group SIR epidemic models with patches through migration and cross patch infection, Acta Math. Sci., 33 (2013), 341-361
##[25]
Y. Muroya, H. Li, T. Kuniya, Complete global analysis of an SIRS epidemic model with graded cure rate and incomplete recovery rate, J. Math. Anal. Appl., 410 (2014), 719-732
##[26]
Y. Nakata, G. Röst, Global analysis for spread of infectious diseases via transportation networks, J. Math. Biol., 70 (2015), 1411-1456
##[27]
J. Ortega, W. Rheinboldt, Monotone iterations for nonlinear equations with application to Gauss-Seidel methods, SIAM J. Numer. Anal., 4 (1967), 171-190
##[28]
H. Shu, D. Fan, J. Wei, Global stability of multi-group SEIR epidemic models with distributed delays and nonlinear transmission, Nonlinear Anal. Rral World Appl., 13 (2012), 1581-1592
##[29]
R. Sun, Global stability of the endemic equilibrium of multigroup SIR models with nonlinear incidence, Comput. Math. Appl., 60 (2010), 2286-2291
##[30]
Y. Takeuchi , Cooperative system theory and global stability of diffusion models, Acta. Appl. Math., 14 (1989), 49-57
##[31]
P. V. D. Driessche, J. Watmough, Reproduction numbers and sub-threshold endemic equilibria for compartmental models of disease transmission, Math. Biosci., 180 (2002), 29-48
##[32]
J. Wang, Y. Takeuchi, S. Liu, A multi-group SVEIR epidemic model with distributed delay and vaccination, Int. J. Biomath., 2012 (2012), 1-18
##[33]
J. Wang, J. Zu, X. Liu, G. Huang, J. Zhang, Global dynamics of a multi-group epidemic model with general relapse distribution and nonlinear incidence rate, J. Biol. Syst., 20 (2012), 235-258
##[34]
W. Wang, L. Chen, Z. Lu , Global stability of a population dispersal in a two-patch environment, Dynam. Systems Appl., 6 (1997), 207-216
##[35]
J. Wang, X. Liu, J. Pang, D. Hou, Global dynamics of a multi-group epidemic model with general exposed distribution and relapse, Osaka J. Math., 52 (2015), 117-138
##[36]
W. Wang, X. Q. Zhao , An epidemic model in a patchy environment, Math. Biosci., 190 (2004), 97-112
##[37]
R. Xu, Z. Ma, Global stability of a SIR epidemic model with nonlinear incidence rate and time delay, Nonlinear Anal. Real World Appl., 10 (2009), 3175-3189
##[38]
Z. Yuan, L. Wang, Global stability of epidemiological models with group mixing and nonlinear incidence rates, Nonlinear Anal. Real World Appl., 11 (2010), 995-1004
##[39]
Z. Yuan, X. Zou, Global threshold property in an epidemic model for disease with latency spreading in a heterogeneous host population, Nonlinear Anal. Real World Appl., 11 (2010), 3479-3490
##[40]
X. Q. Zhao, Z. J. Jing, Global asymptotic behavior in some cooperative systems of functional differential equations, Canad. Appl. Math. Quart., 4 (1996), 421-444
]
Generalized monotone iterative method for integral boundary value problems with causal operators
Generalized monotone iterative method for integral boundary value problems with causal operators
en
en
This paper investigates the existence of solutions for a class of integral boundary value problems with causal
operators. The arguments are based upon the developed monotone iterative method. As applications, two
examples are worked out to demonstrate the main results.
600
609
Wenli
Wang
Department of Information Engineering
China University of Geosciences Great Wall College
People's Republic of China
emilyzh@163.com
Jingfeng
Tian
College of Science and Technology
North China Electric Power University
People's Republic of China
tianjfhxm_ncepu@163.com
Generalized monotone iterative method
integral boundary value problems
causal operators
upper and lower solutions.
Article.12.pdf
[
[1]
B. Ahmad, S. Sivasundaram, Existence of solutions for impulsive integral boundary value problems of fractional order , Nonlinear Anal. Hybrid Syst., 4 (2010), 134-141
##[2]
S. Amini, I. H. Sloan, Collocation methods for second kind integral equations with non-compact operators, J. Integral Equations Appl., 2 (1989), 1-30
##[3]
M. Benchohra, S. Hamani , The method of upper and lower solutions and impulsive fractional differential inclusions, Nonlinear Anal. Hybrid Syst., 3 (2009), 433-440
##[4]
T. G. Bhaskar, F. A. McRae, Monotone iterative techniques for nonlinear problems involving the difference of two monotone functions, Appl. Math. Comput., 133 (2002), 187-192
##[5]
A. Cabada, Z. Hamdi , Nonlinear fractional differential equations with integral boundary value conditions, Appl. Math. Comput., 228 (2014), 251-257
##[6]
J. Han, Y. Liu, J. Zhao , Integral boundary value problems for first order nonlinear impulsive functional integrodifferential differential equations, Appl. Math. Comput., 218 (2012), 5002-5009
##[7]
T. Jankowski, Differential equations with integral boundary conditons, J. Comput. Appl. Math., 147 (2002), 1-8
##[8]
V. Lakshmikantham, S. Leela, Z. Drici, F. A. McRae, Theory of Causal Differential Equations, Atlantis Press, Paris (2010)
##[9]
Z. Liu, J. Han, L. Fang, Integral boundary value problems for first order integro-differential equations with impulsive integral conditions, Comput. Math. Appl., 61 (2011), 3035-3043
##[10]
J. A. Nanware, D. B. Dhaigude, Existence and uniqueness of solutions of differential equations of fractional order with integral boundary conditions, J. Nonlinear Sci. Appl., 7 (2014), 246-254
##[11]
G. Song, Y. Zhao, X. Sun, Integral boundary value problems for first order impulsive integro-differential equations of mixed type, J. Comput. Appl. Math., 235 (2011), 2928-2935
##[12]
T. Wang, F. Xie, Existence and uniqueness of fractional differential equations with integral boundary conditions, J. Nonlinear Sci. Appl., 1 (2008), 206-212
##[13]
P. Wang, S. Tian, Y. Wu , Monotone iterative method for first-order functional difference equations with nonlinear boundary value conditions, Appl. Math. Comput., 203 (2008), 266-2721
##[14]
P. Wang, M. Wu, Oscillation of certain second order nonlinear damped difference equations with continuous variable, Appl. Math. Lett., 20 (2007), 637-644
##[15]
P. Wang, M. Wu, Y. Wu, Practical stability in terms of two measures for discrete hybrid systems, Nonlinear Anal. Hybrid Syst., 2 (2008), 58-64
##[16]
P. Wang, J. Zhang, Monotone iterative technique for initial-value problems of nonlinear singular discrete systems, J. Comput. Appl. Math., 221 (2008), 158-164
##[17]
P. Wang, W. Wang, Anti-periodic boundary value problem for first order impulsive delay difference equations, Adv. Difference Equ., 2015 (2015), 1-13
##[18]
I. H. West, A. S. Vatsala, Generalized monotone iterative method for initial value problems, Appl. Math. Lett., 17 (2004), 1231-1237
##[19]
W. Yang, Positive solutions for nonlinear semipositone fractional q-difference system with coupled integral boundary conditions, Appl. Math. Comput., 244 (2014), 702-725
##[20]
X. Zhang, W. Ge, Positive solutions for a class of boundary-value problems with integral boundary conditions, Comput. Math. Appl., 58 (2009), 203-215
##[21]
X. Zhang, M. Feng, W. Ge , Existence of solutions of boundary value problems with integral boundary conditions for second-order impulsive integro-differential equations in Banach spaces, J. Comput. Appl. Math., 233 (2010), 1915-1926
##[22]
Y. Zhao, G. Song, X. Sun, Integral boundary value problems with causal operators, Comput. Math. Appl., 59 (2010), 2768-2775
]
Fuzzy cone metric spaces
Fuzzy cone metric spaces
en
en
In this study, we define the fuzzy cone metric space, the topology induced by this space and some related
results of them. Also we state and prove the fuzzy cone Banach contraction theorem.
610
616
Tarkan
Öner
Department of Mathematics, Faculty of Sciences
Mugla Sitki Koçman University
Turkey
tarkanoner@mu.edu.tr
Mustafa Burç
Kandemir
Department of Mathematics, Faculty of Sciences
Mugla Sitki Koçman University
Turkey
mbkandemir@mu.edu.tr
Bekir
Tanay
Department of Mathematics, Faculty of Sciences
Mugla Sitki Koçman University
Turkey
btanay@mu.edu.tr
Cone metric space
fuzzy metric space
fuzzy cone metric space
fuzzy cone contractive mapping
Article.13.pdf
[
[1]
A. George, P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets Syst., 64 (1994), 395-399
##[2]
B. Schweizer, A. Sklar, Statistical metric spaces, Pacific J. Maths., 10 (1960), 313-334
##[3]
D. Turkoglu , M. Abuloha , Cone metric spaces and fixed point theorems in diametrically contractive mappings, Acta Math. Sin., 26 (2010), 489-496
##[4]
L. A. Zadeh, Fuzzy sets, Inform. Control, 8 (1965), 338-353
##[5]
L. Huang, X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl., 332 (2007), 1468-1476
##[6]
O. Kramosil, J. Michalek, Fuzzy metric and statistical metric spaces, Kybernetika, 11 (1975), 336-344
##[7]
Sh. Rezapour, R. Hamlbarani, Some notes on the paper ''Cone metric spaces and fixed point theorems of contractive mappings'', J. Math. Anal. Appl., 345 (2008), 719-724
##[8]
V. Gregori, A. Sapena, On fixed-point theorems in fuzzy metric spaces, Fuzzy Sets Syst., 125 (2002), 245-252
]
S-iteration scheme and polynomiography
S-iteration scheme and polynomiography
en
en
The aim of this paper is to present a modification of the visualization process of finding the roots of a
given complex polynomial. In this paper S-iteration scheme is used instead of standard Picard iteration.
The word “polynomiography" coined by Kalantari for that visualization process. The images obtained are
called polynomiographs. Polynomiographs have importance for both the art and science aspects. By using
S-iteration scheme we obtain quite new nicely looking polynomiographs that are different from standard
Picard iteration. Presented examples show that we obtain very interesting patterns for complex polynomial
equations, permutation and doubly stochastic matrices. We believe that the results of this paper enrich the
functionality of the existing polynomiography software.
617
627
Shin Min
Kang
Department of Mathematics and the RINS
Gyeongsang National University
Korea
smkang@gnu.ac.kr
Hamed H.
Alsulami
Nonlinear Analysis and Applied Mathematics Research Group
King Abdulaziz University
Saudi Arabia
hhaalsalmi@kau.edu.sa
Arif
Rafiq
Department of Mathematics
Lahore Leads University
Pakistan
aarafiq@gmail.com
Abdul Aziz
Shahid
Department of Mathematics
Lahore Leads University
Pakistan
abdulazizhanfi@hotmail.com
S-iteration scheme
polynomiography
permutation matrix
doubly stochastic matrix.
Article.14.pdf
[
[1]
R. P. Agarwal, D. O’Regan, D. R. Sahu, Iterative construction of fixed points of nearly asymptotically nonexpansive mappings, J. Nonlinear Convex Anal., 8 (2007), 61-79
##[2]
V. Berinde, Iterative Approximation of Fixed Points, Second Edition, Lectures Notes in Mathematics 1912, Springer-Verlag, Berlin (2007)
##[3]
A. Cayley, The Newton-Fourier imaginary problem, Amer. J. Math., 2 (1879), 1-97
##[4]
S. Ishikawa, Fixed point by a new iteration method, Proc. Amer. Math. Soc., 4 (1974), 147-150
##[5]
G. Julia, Mémoire sur l’iteration des fonctions rationnelles, J. Math. Pures Appl., 8 (1918), 47-246
##[6]
B. Kalantari, Polynomiography: From the Fundamental Theorem of Algebra to Art , Leonardo, 38 (2005), 233-238
##[7]
B. Kalantari, Polynomial Root-finding and Polynomiography, World Scientific Publishing Co. Pte. Ltd., New Jersey (2009)
##[8]
B. Kalantari, Alternating sign matrices and polynomiography, Electron. J. Combin., 2011 (2011), 1-22
##[9]
W. Kotarski, K. Gwawiec, A. Lisoska, Polynomiography via Ishikawa and Mann terations, , 7431 (2012), 305-313
##[10]
B. Mandelbrot, The Fractal Geometry of Nature, W. H. Freeman and Company, New York (1982)
##[11]
W. R. Mann, Mean value methods in iteration, Proc. Amer. Math. Soc., 4 (1953), 506-510
##[12]
H. Minc, Nonnegative Matrices, John Wiley & Sons Inc., New York (1988)
##[13]
H. Susanto, N. Karjanto, Newton’s method’s basins of attraction revisited, Appl. Math. Comput., 215 (2009), 1084-1090
]
On lightlike hypersurfaces and lightlike focal sets of null Cartan curves in Lorentz-Minkowski spacetime
On lightlike hypersurfaces and lightlike focal sets of null Cartan curves in Lorentz-Minkowski spacetime
en
en
In this paper, as a type of event horizons in astrophysics, a class of lightlike hypersurfaces that is generated by
null curves will be investigated and discussed. Based on discussions of the properties of the local differential
geometry of null curves and singularity theory, we provide classifications of the singularities of lightlike
hypersurfaces and lightlike focal sets. In addition, we reveal the facts that the types of these singularities
and the order of contact between a null Cartan curve and a pseudosphere are related closely to null Cartan
curvatures. Finally, examples of lightlike hypersurfaces and lightlike focal set are used to demonstrate our
theoretical results.
628
639
Xinran
Liu
School of Mathematical Sciences
Harbin Normal University
P. R. China
Zhigang
Wang
School of Mathematical Sciences
College of Mathematics
Harbin Normal University
Jilin University
P. R. China
P. R. China
wangzg2003205@163.com
null Cartan curve
lightlike hypersurface
singularity
Article.15.pdf
[
[1]
J. M. Bardeen, B. Carter, S. W. Hawking, The four laws of black hole mechanics, Comm. Math. Phys., 31 (1973), 161-170
##[2]
J. W. Bruce, P. J. Giblin, Curves and Singularities, Cambridge University Press, Cambridge (1992)
##[3]
A. C. CÖken, Ü. CiftCi, On the Cartan curvatures of a null curve in Minkowski spacetime, Geom. Dedicata, 114 (2005), 71-78
##[4]
G. Clement , Black holes with a null Killing vector in three-dimensional massive gravity, Class. Quantum Grav., 2009 (2009), 1-11
##[5]
M. M. de Souza, The Lorentz-Dirac equation and the structures of spacetime, Braz. J. Phys., 28 (1998), 250-256
##[6]
K. L. Duggal, A. Bejancu, Lightlike Submanifolds of Semi-Riemannian Manifolds and Applications, Dordrecht, The Netherlands (1996)
##[7]
K. L. Duggal, Constant curvature and warped product globally null manifolds, J. Geom. Phy. , 43 (2002), 327-340
##[8]
K. L. Duggal, On scalar curvature in lightlike geometry, J. Geom. Phy., 57 (2007), 473-481
##[9]
K. L. Duggal, A Report on canonical null curves and screen distributions for lightlike geometry, Acta Appl. Math., 95 (2007), 135-149
##[10]
E. Gourgoulhon, J. L. Jaramillo, A 3 + 1 perspective on null hypersurfaces and isolated horizons, Phys. Rep., 423 (2006), 159-294
##[11]
S. W. Hawking, Black holes in general relativity, Comm. Math. Phys., 25 (1972), 152-166
##[12]
S. Izumiya, T. Sato, Lightlike hypersurfaces along spacelike submanifolds in Minkowski space-time, J. Geom. Phys., 71 (2013), 30-52
##[13]
M. Korzynski, J. Lewandowski, T. Pawlowski, Mechanics of multidimensional isolated horizons, Class. Quantum Grav., 22 (2005), 2001-2016
##[14]
A. Nersessian, E. Ramos, Massive spinning particles and the geometry of null curves, Phys. Lett. B, 445 (1998), 123-128
##[15]
A. Nersessian, E. Ramos, A geometrical particle model for anyons, Modern Phys. Lett. A, 14 (1999), 2033-2037
##[16]
W. Rudnicki , Black hole interiors cannot be totally vicious , Phys. Lett. A, 208 (1995), 53-58
##[17]
W. Rudnicki, R. J. Budzynski, W. Kondracki, Generalized strong curvature singularities and weak cosmic censorship in cosmological space-times, Mod. Phys. Lett. A., 21 (2006), 1501-1509
##[18]
J. Sultana, C. C. Dyer, Cosmological black holes: A black hole in the Einstein-de Sitter universe, Gen. Relativ. Gravit., 37 (2005), 1349-1370
##[19]
J. Sun, D. Pei, Null Cartan Bertrand curves of AW(k)-type in Minkowski 4-space, Phys. Lett. A, 376 (2012), 2230-2233
##[20]
J. Sun, D. Pei, Some new properties of null curves on 3-null cone and unit semi-Euclidean 3-spheres, J. Nonlinear Sci. Appl., 8 (2015), 275-284
##[21]
S. I. Tertychniy , The black hole formed by electromagnetic radiation, Phys. Lett. A, 96 (1983), 73-75
##[22]
M. Vincent, I. James, Symmetries of cosmological Cauchy horizons, Comm. Math. Phys., 89 (1983), 387-413
##[23]
Z. Wang, D. Pei , Singularities of ruled null surfaces of the principal normal indicatrix to a null Cartan curve in de Sitter 3-space, Phys. Lett. B, 689 (2010), 101-106
##[24]
Z. Wang, D. Pei, Geometry of 1-lightlike submanifolds in anti de Sitter n-space, Proc. Roy. Soc. Edinburgh Sect. A, 143 (2013), 1089-1113
##[25]
Z. Wang, D. Pei, L. Kong, Gaussian surfaces and nullcone dual surfaces of null curves in a three-dimensional nullcone with index 2, J. Geom. Phys., 73 (2013), 166-186
]
The general solution of a quadratic functional equation and Ulam stability
The general solution of a quadratic functional equation and Ulam stability
en
en
In this paper, we investigate the general solution of a new quadratic functional equation. We prove that
a function admits, in appropriate conditions, a unique quadratic mapping satisfying the corresponding
functional equation. Finally, we discuss the Ulam stability of that functional equation by using the directed
method and fixed point method, respectively.
640
649
Yaoyao
Lan
College of Computer Science
Key Laboratory of Chongqing University of Arts and Sciences
Chongqing University
China
China
yylanmath@163.com
Yonghong
Shen
School of Mathematics and Statistics
Tianshui Normal University
China
shenyonghong2008@hotmail.com
functional equation
Ulam stability
quadratic mapping.
Article.16.pdf
[
[1]
T. Aoki , On the stability of the linear transformation in Banach spaces, J. Math. Soc. Japan, 2 (1950), 64-66
##[2]
D. Barbu, C. Buse, A. Tabassum, Hyers-Ulam stability and discrete dichotomy, J. Math. Anal. Appl., 423 (2015), 1738-1752
##[3]
S. Czerwik, Functional Equations and Inequalities in Several Variables, World Scientific, Singapore (2000)
##[4]
K. Cieplinski, On the generalized Hyers-Ulam stability of multi-quadratic mappings, Comput. Math. Appl., 62 (2011), 3418-3426
##[5]
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
##[6]
D. H. Hyers , On the stability of the linear functional equation, Proc. Nat. Acad. Sci. USA, 27 (1941), 222-224
##[7]
D. H. Hyers, G. Isac, T. M. Rassias, Stability of Functional Equations in Several Variables, Birkhäuser , Boston (1998)
##[8]
S. M. Jung, Hyers-Ulam-Rassias Stability of Functional Equations in Nonlinear Analysis, Springer, New York (2011)
##[9]
S. M. Jung, On the Hyers-Ulam-Rassias stability of a quadratic functional equation , J. Math. Anal. Appl., 232 (1999), 384-393
##[10]
S. M. Jung, On the Hyers-Ulam stability of the functional equations that have the quadratic property, J. Math. Anal. Appl., 222 (1998), 126-137
##[11]
H. A. Kenary, H. Rezaei, Y. Gheisari, C. Park, On the stability of set-valued functional equations with the fixed point alternative, Fixed Point Theory Appl., 2012 (2012), 1-17
##[12]
Y. W. Lee, On the stability of a quadratic Jensen type functional equation, J. Math. Anal. Appl., 270 (2002), 590-601
##[13]
A. K. Mirmostafaee, M. S. Moslehian, Fuzzy versions of Hyers-Ulam-Rassias theorem, Fuzzy Set. Sys., 159 (2008), 720-729
##[14]
M. S. Moslehian, T. M. Rassias, Stability of functional equations in non-Archimedean spaces, Appl. Anal. Discrete Math., 1 (2007), 325-334
##[15]
K. Nikodem, D. Popa, On single-valuedness of set-valued maps satisfying linear inclusions, Banach J. Math. Anal., 3 (2009), 44-51
##[16]
C. G. Park, On the Hyers-Ulam-Rassias stability of generalized quadratic mappings in Banach modules , J. Math. Anal. Appl., 291 (2004), 214-223
##[17]
C. Park, H. A. Kenary, T. M. Rassias , Hyers-Ulam-Rassias stability of the additive-quadratic mappings in non- Archimedean Banach spaces, J. Inequal. Appl., 2012 (2012), 1-18
##[18]
T. M. Rassias, On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72 (1978), 297-300
##[19]
V. Radu, The fixed point alternative and the stability of functional equations, Fixed Point Theory, 4 (2003), 91-96
##[20]
H. Y. Shen, Y. Y. Lan, On the general solution of a quadratic functional equation and its Ulam stability in various abstract spaces, J. Nonlinear Sci. Appl., 7 (2014), 368-378
##[21]
S. M. Ulam, Problems in Modern Mathematics, Wiley, New York (1964)
]
Solutions for a nonlinear fractional boundary value problem with sign-changing Greens function
Solutions for a nonlinear fractional boundary value problem with sign-changing Greens function
en
en
This paper considers the existence, uniqueness and non-existence of solution for a quasi-linear fractional
boundary value problems with sign-changing Green’s function. Under certain growth conditions on the
nonlinear term, we employ the Leray-Schauder alternative fixed point theorem to obtain an existence result
of nontrivial solution and use the Banach contraction mapping principle to obtain a uniqueness result.
Moreover, the existence result of positive solutions is obtained when the nonlinear term is also allowed to
change sign.
650
659
Youzheng
Ding
Department of Mathematics
Shandong Jianzhu University
China
dingyouzheng@163.com
Zhongli
Wei
Department of Mathematics
Shandong Jianzhu University
China
jnwzl32@163.com
Qingli
Zhao
Department of Mathematics
Shandong Jianzhu University
China
zhaoqingliabc@163.com
Fractional boundary value problem
fixed point theorem
sign-changing Green’s function
positive solution
existence.
Article.17.pdf
[
[1]
J. Bai, X. Feng, Fractional-order anisotropic diffusion for image denoising, IEEE Trans. Signal Process., 16 (2007), 2492-2502
##[2]
T. Chen, W. Liu, An anti-periodic boundary value problem for the fractional differential equation with a p- Laplacian operator, Appl. Math. Lett., 25 (2012), 1671-1675
##[3]
M. El-Shahed, J. Nieto, Nontrivial solutions for a nonlinear multi-point boundary value problem of fractional order, Comput. math. appl., 59 (2010), 3438-3443
##[4]
J. Graef, L. Kong, Q. Kong, M. Wang , Existence and uniqueness of solutions for a fractional boundary value problem with Dirichlet boundary condition, Electron. J. Qual. Theory Differ. Equ., 2013 (2013), 1-11
##[5]
D. Guo, V. Lakshmikantham, Nonlinear Problems in Abstract Cones, Academic Press, Boston (1988)
##[6]
Y. He, L. Yue, Positive solutions for Neumann boundary value problems of nonlinear second-order integrodifferential equations in ordered Banach spaces, J. Inequal. Appl., 2011 (2011), 1-11
##[7]
D. Jiang, C. Yuan, The positive properties of the Green function for Dirichlet-type boundary value problems of nonlinear fractional differential equations and its application, Nonlinear Anal. TMA., 72 (2010), 710-719
##[8]
A. Kilbas, H. Srivastava, J. Trujillo , Theory and Applications of Fractional Differential Equations, in: North- Holland Mathematics Studies, Elsevier Science B. V., Amsterdam (2006)
##[9]
J. Liu, M. Xu, Higher-order fractional constitutive equations of viscoelastic materials involving three different parameters and their relaxation and creep functions, Mech. Time-Depend Mater., 10 (2006), 263-279
##[10]
H. Lu, Z. Han, S. Sun, J. Liu, Existence on positive solutions for boundary value problems of nonlinear fractional differential equations with p-Laplacian, Adv. Difference Equ., 2013 (2013), 1-16
##[11]
Y. Li, Positive solutions of fourth-order boundary-value problem with two parameters, J. Math. Anal. Appl., 281 (2003), 477-484
##[12]
R. Magin, Fractional calculus models of complex dynamics in biological tissues, Comput. Math. Appl. , 59 (2010), 1586-1593
##[13]
I. Podlubny, Fractional Differential Equations, Academic Press, San Diego (1999)
##[14]
M. Rehman, R. Khan, Existence and uniqueness of solutions for multi-point boundary value problems for fractional differential equations, Appl. Math. Lett., 23 (2010), 1038-1044
##[15]
G. Wang, B. Ahmad, L. Zhang, Impulsive anti-periodic boundary value problem for nonlinear differential equations of fractional order, Nonlinear Anal., 74 (2011), 792-804
##[16]
G. Wang, S. Ntouyas, L. Zhang, Positive solutions of the three-point boundary value problem for fractional-order differential equations with an advanced argument, Adv. Difference Equ., 2011 (2011), 1-11
##[17]
Z. Wei, W. Dong, J. Che, Periodic boundary value problems for fractional differential equations involving a Riemann-Liouville fractional derivative, Nonlinear anal., 73 (2010), 3232-3238
##[18]
J. Wang, H. Xiang , Upper and lower solutions method for a class of singular fractional boundary value problems with p-Laplacian operator, Abstr. Appl. Anal., 2010 (2010), 1-12
##[19]
J. Wei , Eigenvalue interval for multi-point boundary value problems of fractional differential equations, Appl. Math. Comput., 219 (2013), 4570-4575
##[20]
Z. Wei, C. Pang, Y. Ding, Positive solutions of singular Caputo fractional differential equations with integral boundary conditions, Commun. Nonlinear Sci. Numer. Simul., 17 (2012), 3148-3160
##[21]
X. Xu, D. Jiang, C. Yuan, Multiple positive solutions for the boundary value problem of a nonlinear fractional differential equation, Nonlinear Anal., 71 (2009), 4676-4688
##[22]
D. Yan, Z. Pan, Positive solutions of nonlinear operator equations with sign-changing kernel and its applications, Appl. Math. Comput., 230 (2014), 675-679
##[23]
X. Zhang, L. Liu, Y. Wu, The uniqueness of positive solution for a singular fractional differential system involving derivatives, Commun. Nonlinear Sci. Numer. Simul., 18 (2013), 1400-1409
##[24]
S. Zhong, Y. An, Existence of positive solutions to periodic boundary value problems with sign-changing Green’s function, Bound. Value Probl., 2011 (2011), 1-6
##[25]
X. Zhang, L. Liu, Y. Wu, The eigenvalue problem for a singular higher order fractional differential equation involving fractional derivatives, Appl. Math. Comput., 2012 (218), 8526-8536
##[26]
S. Zhang, Positive solutions to singular boundary value problem for nonlinear fractional differential equation, Comput. Math. Appl., 59 (2010), 1300-1309
]
Newton method for estimation of the Robin coefficient
Newton method for estimation of the Robin coefficient
en
en
This paper considers estimation of Robin parameter by using measurements on partial boundary and solving
a Robin inverse problem associated with the Laplace equation. Typically, such problems are solved utilizing
a Gauss-Newton method in which the forward model constraints are implicitly incorporated. Variants
of Newton’s method which use second derivative information are rarely employed because their perceived
disadvantage in computational cost per step offsets their potential benefits of fast convergence. In this paper,
we show that by formulating the inversion as a constrained or unconstrained optimization problem, we can
carry out the sequential quadratic programming and the full Newton iteration with only a modest additional
cost. Our numerical results illustrate that Newton’s method can produce a solution in fewer iterations and,
in some cases where the data contain significant noise, requires fewer floating point operations than Gauss-
Newton methods.
660
669
Yan-Bo
Ma
Department of Mathematics and Statist
Hanshan Normal University
P. R. China
yanboma@hstc.edu.cn
Robin inverse problem
ill-posedness
boundary integral equations
Newton method
Gauss-Newton method.
Article.18.pdf
[
[1]
G. Alessandrini, L. Del Piero, L. Rondi , Stable determination of corrosion by single electrostatic boundary measurement, Inverse Problems, 19 (2003), 973-984
##[2]
U. Ascher, R. Mattheij, R. Russell , Numerical Solution of Boundary Value Problems for Ordinary Differential Equations, SIAM, Philadelphia (1995)
##[3]
K. Atkinson, The Numerical Solution of Integral Equation of Second Kind, Cambridge University Press, Cambridge (1997)
##[4]
S. Busenberg, W. Fang, Identification of semiconductor contact resistivity, Quart. Appl. Math., 49 (1991), 639-649
##[5]
S. Chaabane, C. Elhechmi, M. Jaoua, A stable recovery method for the Robin inverse problem, Math.Comput. Simulation, 66 (2004), 367-383
##[6]
S. Chaabane, I. Feki, N. Mars, Numerical reconstruction of a piecewise constant Robin parameter in the two- or three-dimensional case, Inverse Problems, 28 (2012), 1-19
##[7]
S. Chaabane, I. Fellah, M. Jaoua, J. Leblond, Logarithmic stability estimates for a Robin coefficient in twodimensional Laplace inverse problems, Inverse Problems, 20 (2004), 47-59
##[8]
S. Chaabane, J. Ferchichi, K. Kunisch, Differentiability properties of \(L^1\)-tracking functional and application to the Robin inverse problem, Inverse Problems, 20 (2004), 1083-1097
##[9]
S. Chaabane, M. Jaoua, Identification of Robin coefficients by means of boundary measurements, Inverse Problems, 15 (1999), 1425-1438
##[10]
L. M. Delves, J. L. Mohamed , Computational Methods for Integral Equations, Cambridge University Press, Appendix A , Cambridge (1985)
##[11]
J. E. Dennis, M. Heinkenschloss, L. N. Vicente, Trust-region interior-point SQP algorithms for a class of nonlinear programming problems, SIAM J. Control Optim., 36 (1998), 1750-1794
##[12]
W. Fang, E. Cumberbatch, Inverse problems for metal oxide semiconductor field-effect transistor contact resistivity, SIAM J. Appl. Math., 52 (1992), 699-709
##[13]
W. Fang, X. Zeng, A direct solution of the Robin inverse problem, J. Integral Equations Appl., 21 (2009), 545-557
##[14]
D. Fasino, G. Inglese, An inverse Robin problem for Laplace’s equation: theoretical results and numerical methods, Inverse Problems, 15 (1999), 41-48
##[15]
D. Fasino, G. Inglese, Discrete methods in the study of an inverse problem for Laplace’s equation, SIAM J. Numer. Anal., 19 (1999), 105-118
##[16]
E. Haber, Numerical strategies for the solution of inverse problems, PhD thesis, University of British Columbia (1998)
##[17]
E. Haber, U. M. Ascher, D. Oldenburg, On optimization techniques for solving nonlinear inverse problems, Inverse problems, 16 (2000), 1263-1280
##[18]
M. Heinkenschloss, Mesh independence for nonlinear least squares problems with norm constraints, SIAM J. Optim., 3 (1993), 81-117
##[19]
G. Inglese, An inverse problem in corrosion detection, Inverse Problems, 13 (1997), 977-994
##[20]
B. Jin, Conjugate gradient method for the Robin inverse problem associated with the Laplace equation, Internat. J. Numer. Methods Engrg, 71 (2007), 433-453
##[21]
B. Jin, J. Zou, Inversion of Robin coefficient by a spectral stochastic finite element approach, J. Comput. Phys., 227 (2008), 3282-3306
##[22]
B. Jin, J. Zou, Numerical estimation of piecewise constant Robin coefficient, SIAM J. Control Optim., 48 (2009), 1977-2002
##[23]
P. G. Kaup, F. Santosa, Nondestructive evaluation of corrosion damage using electrostatic measurements, J. Nondestruct. Eval., 14 (1995), 127-136
##[24]
R. Kress, Linear Integral Equations, Springer, New York (1999)
##[25]
F. Lin, W. Fang, A linear integral equation approach to the Robin inverse problem, Inverse Problems, Appendix A , 21 (2005), 1757-1772
##[26]
W. H. Loh, K. Saraswat, R. W. Dutton, Analysis and scaling of Kelvin resistors for extraction of specific contact resistivity, IEEE Electron. Device Lett., 1985 (6), 105-108
##[27]
W. H. Loh, S. E. Swirhun, T. A. Schreyer, R. M. Swanson, K. C. Saraswat, Modeling and measurement of contact resistances, IEEE Transac. Elect. Dev., 34 (1987), 512-524
##[28]
V. G. Maz’ya, Boundary integral equations analysis IV, Springer, New York (1991)
##[29]
J. Nocedal, S. Wright , Numerical Optimization, Springer, New York (2006)
##[30]
F. Santosa, M. Vogelius, J. M. Xu, An effective nonlinear boundary condition for corroding surface identification of damage based on steady state electric data , Z. Angew. Math. Phys., 49 (1998), 656-679
]
Some fixed point results for nonlinear mappings in convex metric spaces
Some fixed point results for nonlinear mappings in convex metric spaces
en
en
In this paper, we consider an iteration process to approximate a common random fixed point of a finite
family of asymptotically quasi-nonexpansive random mappings in convex metric spaces. Our results extend
and improve several known results in recent literature.
670
677
Chao
Wang
School of Mathematics and Statistics
Nanjing University of Information Science and Technology
P. R. China
wangchaosx@126.com
Asymptotically quasi-nonexpansive random mappings
random iteration process
common random fixed point
convex metric spaces.
Article.19.pdf
[
[1]
I. Beg , Approximation of random fixed point in normed space, Nonlinear Anal., 51 (2002), 1363-1372
##[2]
I. Beg, M. Abbas, Iterative procedures for solutions of random operator equations in Banach space, J. Math. Anal. Appl., 315 (2006), 180-201
##[3]
A. T. Bharucha-Reid , Random integral equation, Academic Press, New York (1972)
##[4]
B. L. Ciric, J. S. Ume, M. S. Khan, On the convergence of the Ishikawa iterates to a common fixed point of two mappings, Arch. Math., 39 (2003), 123-127
##[5]
B. S. Choudhury, Convergence of a random iteration scheme to random fixed point, J. Appl. Math. Stoch. Anal., 8 (1995), 139-142
##[6]
B. S. Choudhury, Random Mann iteration scheme, Appl. Math. Lett., 16 (2003), 93-96
##[7]
O. Hans, Random operator equations, University of California Press, Calif (1961)
##[8]
S. Itoh, Random fixed point theorems with an application to random differential equations in Banach space, J. Math. Anal. Appl., 67 (1979), 261-273
##[9]
A. R. Khan, A. A. Domb, H. Fukhar-ud-din, Common fixed points Noor iteration for a finite family of asymptotically quasi-nonexpansive mappings in Banach space, J. Math. Anal. Appl., 341 (2008), 1-11
##[10]
A. R. Khan, M. A. Ahmed, Convergence of a general iterative scheme for a finite family of asymptotically quasi- nonexpansive mappings in convex metric spaces and applications, Comput. Math. Appl., 59 (2010), 2990-2995
##[11]
P. Kumam, S. Plubtieng, Some random fixed point theorems for non-self nonexpansive random operators, Turkish J. Math., 30 (2006), 359-372
##[12]
P. Kumam, S. Plubtieng, Random fixed point theorems for asymptotically regular random operators, Dem. Math., 40 (2009), 131-141
##[13]
P. Kumam, S. Plubtieng, The characteristic of noncompact convexity and random fixed point theorem for set- valued operators, Czechoslovak Math. J., 57 (2007), 269-279
##[14]
P. Kumam, W. Kumam , Random fixed points of multivalued random operators with property (D), Random Oper. Stoch. Equ., 15 (2007), 127-136
##[15]
Q. H. Liu , Iterative sequences for asymptotically quasi-nonexpansive mapping with errors memeber, J. Math. Anal. Appl., 259 (2001), 18-24
##[16]
S. Plubtieng, P. Kumam, R. Wangkeeree, Approximation of a common random fixed point for a finite family of random operators, Int. J. Math. Math. Sci., 2007 (2007), 1-12
##[17]
P. L. Ramirez, Random fixed points of uniformly Lipschitzian mappings, Nonlinear Anal., 57 (2004), 23-34
##[18]
A. Spacek, Zufallige gleichungen, Czechoslovak Math. J., 5 (1955), 462-466
##[19]
W. Takahashi, A convexity in metric space and nonexpansive mapping, I. Kodai Math. Sem. Rep., 22 (1970), 142-149
##[20]
K. K. Tan, X. Z. Yuan, Some random fixed point theorems, Fixed Point Theory Appl., (1991), 334-345
##[21]
C. Wang, L. W. Liu, Convergence theorems for fixed points of uniformly quasi-Lipschitzian mappings in convex metric spaces, Nonlinear Anal, 70 (2009), 2067-2071
##[22]
I. Yildirim, S. H. Khan, Convergence theorems for common fixed points of asymptotically quasi-nonexpansive mappings in convex metric spaces, Appl. Math. Comput., 218 (2012), 4860-4866
]
Evolutes of fronts on Euclidean 2-sphere
Evolutes of fronts on Euclidean 2-sphere
en
en
We define framed curves (or frontals) on Euclidean 2-sphere, give a moving frame of the framed curve and
define a pair of smooth functions as the geodesic curvature of a regular curve. It is quite useful for analysing
curves with singular points. In general, we can not define evolutes at singular points of curves on Euclidean
2-sphere, but we can define evolutes of fronts under some conditions. Moreover, some properties of such
evolutes at singular points are given.
678
686
Haiou
Yu
School of Mathematics and Statistics
Department of Mathematical Education, College of Humanities and Sciences
Northeast Normal University
Northeast Normal University
P. R. China
P. R. China
yuho930@nenu.edu.cn
Donghe
Pei
School of Mathematics and Statistics
Northeast Normal University
P. R. China
peidh340@nenu.edu.cn
Xiupeng
Cui
School of Mathematics and Statistics
Northeast Normal University
P. R. China
cuixp606@nenu.edu.cn
framed curve
evolute
front.
Article.20.pdf
[
[1]
V. I. Arnold, S. M. Gusein-Zade, A. N. Varchenko, Singularities of differentiable maps, Springer, New York (1985)
##[2]
V. I. Arnold, Topological properties of Legendre projections in contact geometry of wave fronts, St. Petersburg Math. J., 6 (1995), 439-452
##[3]
V. I. Arnold, Singularities of caustics and wave fronts, Kluwer Academic Publishers, Dordrecht (1990)
##[4]
J. W. Bruce, P. J. Giblin, Curves and singularities, Cambridge University Press, Cambridge (1992)
##[5]
X. Cui, D. Pei, H. Yu, Evolutes of fronts in hyperbolic plane, Preprint, (2015)
##[6]
J. Ehlers, E. T. Newman, The theory of caustics and wave front singularities with physical applications , J. Math. Phys., 41 (2000), 3344-3378
##[7]
D. Fuchs, Evolutes and involutes of spatial curves, Amer. Math. Monthly, 120 (2013), 217-231
##[8]
T. Fukunaga, M. Takahashi, Existence and uniqueness for Legendre curves, J. Geom., 104 (2013), 297-307
##[9]
T. Fukunaga, M. Takahashi, Evolutes and involutes of frontals in the Euclidean plane, Preprint, (2013)
##[10]
C. G. Gibson, Elementary geometry of differentiable curves, Cambridge University Press, Cambridge (2001)
##[11]
A. Gray, E. Abbena, S. Salamon, Modern differential geometry of curves and surfaces with Mathematica Chapman and Hall/CRC, Boca Raton, FL (2006)
##[12]
S. Izumiya, D. Pei, T. Sano, E. Torii , Evolutes of hyperbolic plane curves, Acta Math. Sin. (Engl. Ser.), 20 (2004), 543-550
##[13]
G. Ishikawa, S. Janeczko, Symplectic bifurcations of plane curves and isotropic liftings, Q. J. Math., 54 (2003), 73-102
##[14]
M. Külahc, M. Ergüt, Bertrand curves of AW(k)-type in Lorentzian space, Nonlinear Anal., 70 (2009), 1725-1731
##[15]
J. Sun, D. Pei, Some new properties of null curves on 3-null cone and unit semi-Euclidean 3-spheres, J. Nonlinear Sci. Appl., 8 (2015), 275-284
]
Fixed point theorems for (\(\psi\circ\varphi\))-contractions in a fuzzy metric spaces
Fixed point theorems for (\(\psi\circ\varphi\))-contractions in a fuzzy metric spaces
en
en
In this paper we prove some common fixed point theorems for (\(\psi\circ\varphi\))− contractions in a fuzzy metric space.
We offered a generalization of \(\varphi\)− contraction in fuzzy metric space. Our results generalize or improve many
recent fixed point theorems in the literature.
687
694
Muzeyyen
Sangurlu
Department of Mathematics, Faculty of Science
Department of Mathematics, Faculty of Science and Arts
University of Gazi
University of Giresun
Turkey
Turkey
msangurlu@gazi.edu.tr
Duran
Turkoglu
Department of Mathematics, Faculty of Science and Arts
University of Giresun
Turkey
dturkoglu@gazi.edu.tr
Fixed point theorem
fuzzy metric spaces
contractions
Article.21.pdf
[
[1]
A. Aliouche, F. Merghadi, A. Djoudi , A related fixed point theorem in two fuzzy metric spaces, J. Nonlinear Sci. Appl., 2 (2009), 19-24
##[2]
I. Altun, D. Mihet, Ordered non-Archimedean fuzzy metric spaces and some fixed point results, Fixed Point Theory Appl., 2010 (2010), 1-11
##[3]
M. S. Chauan, V. H. Badshah, V. S. Chouhan, Common fixed point of semi compatible maps in fuzzy metric spaces, Kathmandu Uni. J. Sci. Engin. Tech., 6 (2010), 70-78
##[4]
C. Di Bari, C. Vetro, Fixed points, attractors and weak fuzzy contractive mappings in a fuzzy metric space, J. Fuzzy Math., 13 (2005), 973-982
##[5]
Z. Deng, Fuzzy pseudometric spaces, J. Math. Anal. Appl., 86 (1982), 74-95
##[6]
A. George, P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets and Systems, 64 (1994), 395-399
##[7]
A. George, P. Veeramani, On some results of analysis for fuzzy metric spaces, Fuzzy Sets and Systems, 90 (1997), 365-368
##[8]
D. Gopal, M. Imdad, C. Vetro, M. Hasan, Fixed point theory for cyclic weak ϕ-contraction in fuzzy metric spaces, J. Nonlinear Anal. Appl., 2012 (2012), 1-11
##[9]
M. Grabiec, Fixed points in fuzzy metric spaces, Fuzzy Sets and Systems, 27 (1988), 385-389
##[10]
V. Gregori, A. Sapena, On fixed-point theorems in fuzzy metric spaces, Fuzzy Sets and Systems, 125 (2002), 245-252
##[11]
S. Jain, S. Jain, L. B. Jain, Compatibility of type (P) in modified intuitionistic fuzzy metric space, J. Nonlinear Sci. Appl., 3 (2010), 96-109
##[12]
W. A. Kirk, P. S. Srinavasan, P. Veeramani, Fixed points for mapping satisfying cyclical contractive conditions, Fixed Point Theoery, 4 (2003), 79-89
##[13]
I. Kramosil, J. Michalek, Fuzzy metric and statistical metric spaces, Kybernetica, 11 (1975), 336-344
##[14]
H. K. Nashine, Z. Kadelburg, Fixed point theorems using cyclic weaker meir-keeler functions in partial metric spaces, Filomat, 28 (2014), 73-83
##[15]
M. Păcurar, I. A. Rus, Fixed point theory for cyclic ϕ-contractions, Nonlinear Anal., 72 (2010), 1181-1187
##[16]
K. P. R. Rao, A. Aliouche, G. R. Babu , Related fixed point theorems in fuzzy metric spaces, J. Nonlinear Sci. Appl., 1 (2008), 194-202
##[17]
B. Schweizer, A. Sklar , Statistical metric spaces, Pacific J. Math., 10 (1960), 313-334
##[18]
Y. H. Shen, D. Qiu, W. Chen, Fixed point theory for cyclic ϕ-contractions in fuzzy metric spaces, Iran. J. Fuzzy Syst., 10 (2013), 125-133
##[19]
D. Turkoglu, M. Sangurlu , Fixed point theorems for fuzzy \(\psi\)-contractive mappings in fuzzy metric spaces, J. Intell. Fuzzy Syst., 26 (2014), 137-142
##[20]
R. Vasuki, P. Veeramani , Fixed point theorems and Cauchy sequences in fuzzy metric spaces, Fuzzy Sets and Systems, 135 (2003), 415-417
##[21]
C. Vetro, Fixed points in a weak non-Archemedean fuzzy metric spaces, Fuzzy Sets and Systems, 162 (2011), 84-90
]
A global optimization approach for a class of MINLP problems with applications to crude oil scheduling problem
A global optimization approach for a class of MINLP problems with applications to crude oil scheduling problem
en
en
A global optimization algorithm is proposed to solve the crude oil schedule problem. We first developed
a lower and upper bounding model by using a multiparametric disaggregation method. Secondly, the
lower and the upper bounding models combined with finite state method (FSM) are incorporated to solve
the bilinear programing problem jointly. The advantage of using FSM is that we can generate promising
substructure and partial solution. Furthermore, the FSM can guarantee that the entire solution space is
uniformly covered. Therefore, the algorithm has better global performance than some existing algorithms.
Finally, a real-life crude oil scheduling problem from the literature is used for conducting simulation. The
experimental results validate that the proposed method outperforms commercial solvers.
695
709
Qianqian
Duan
Department of Automation
Shanghai Jiao Tong University
China
dqq1019@sjtu.edu.cn
Genke
Yang
Department of Automation
Shanghai Jiao Tong University
China
sjtu1019@163.com
Guanglin
Xu
College of Mathematics and Information
Shanghai Lixin University of Commerce
China
glxu@outlook.com
Xueyan
Duan
School of Economics and Management
Shanghai Maritime University
China
328236505@qq.com
MINLP
finite state method
hybrid optimization.
Article.22.pdf
[
[1]
F. A. Al-Khayyal, J. E. Falk, Jointly Constrained Biconvex Programming , Math. Oper. Res., 8 (1983), 273-286
##[2]
N. Adhya, M. Tawarmalani, N. V. Sahinidis, A Lagrangian Approach to the Pooling Problem, Indu. Eng. Chem. Res., 38 (1999), 1956-1972
##[3]
M. L. Bergamini, P. Aguirre, I. Grossmann, Logic-based outer approximation for globally optimal synthesis of process networks, Comput. Chem. Eng., 29 (2005), 1914-1933
##[4]
E. D. Dolan, J. J. Mor, Benchmarking optimization software with performance prfiles , Math. Program., 91 (2002), 201-213
##[5]
I. E. Grossmann, Review of Nonlinear Mixed-Integer and Disjunctive Programming Techniques, Optim. Eng., 3 (2002), 227-252
##[6]
R. Horst, H. Tuy, Global optimization: Deterministic approaches, Springer, Berlin (1996)
##[7]
S. Kolodziej, P. M. Castro, I. E. Grossmann, Global optimization of bilinear programs with a multiparametric disaggregation technique, J. Global Optim., 57 (2013), 1039-1063
##[8]
H. Lee, J. M. Pinto, I. E. Grossmann, S. Park, Mixed-integer linear programming model for refinery short-term scheduling of crude oil unloading with inventory management , Ind. Eng. Chem. Res., 35 (1996), 1630-1641
##[9]
L. Liberti, S. Cafieri, F. Tarissan, Reformulations in Mathematical Programming: A Computational Approach, Found. Comput. Intell., 203 (2009), 153-234
##[10]
L. Liberti, C. C. Pantelides, An Exact Reformulation Algorithm for Large Nonconvex NLPs Involving Bilinear Terms, J. Global Optim., 36 (2006), 161-189
##[11]
R. Misener, C. Floudas, GloMIQO: Global mixed-integer quadratic optimizer, J. Global Optim., 57 (2013), 3-50
##[12]
S. Mouret, I. E. Grossmann, P. Pestiaux, A Novel Priority-Slot Based Continuous-Time Formulation for Crude- Oil Scheduling Problems, Ind. Eng. Chem. Res., 48 (2009), 8515-8528
##[13]
Y. Nesterov, Semidefinite relaxation and nonconvex quadratic optimization , Optim. Meth. Softw, 9 (1998), 141-160
##[14]
M. Oral, O. Kettani , A Linearization Procedure for Quadratic and Cubic Mixed-Integer Problems, Oper. Res., 40 (1992), 109-116
##[15]
M. Pan, Y. Qian, X. Li , Flexible scheduling model of crude oil operations under crude supply disturbance, Science in China, 52 (2009), 387-400
##[16]
H. S. Ryoo, N. V. Sahinidis, Global optimization of nonconvex NLPs and MINLPs with applications in process design, Comput. Chem. Eng., 19 (1995), 551-566
##[17]
H. Sherali, A. Alameddine, A new reformulation-linearization technique for bilinear programming problems, J. Global Optim., 2 (1992), 379-410
##[18]
N. Z. Shor, Dual quadratic estimates in polynomial and Boolean programming, Ann. Oper. Res., 25 (1990), 163-168
##[19]
M. Tawarmalani, N. V. Sahinidis, A polyhedral branch-and-cut approach to global optimization, Math. Program, 103 (2005), 225-249
##[20]
J. P. Teles, P. M. Castro, H. A. Matos, Multi-parametric disaggregation technique for global optimization of polynomial programming problems, J. Global Optim., 55 (2013), 227-251
##[21]
G. Van Noord, FSA Utilities: A toolbox to manipulate finite-state automata, Automata Implementation, 1260 (1997), 87-108
##[22]
D. S. Wicaksono, I. A. Karimi , Piecewise MILP under- and overestimators for global optimization of bilinear programs, AIChE J., 54 (2008), 991-1008
]
On the Ulam stability of the Cauchy-Jensen equation and the additive-quadratic equation
On the Ulam stability of the Cauchy-Jensen equation and the additive-quadratic equation
en
en
In this paper, we investigate the Ulam stability of the functional equations
\[2f ( x + y; \frac{z + w}{ 2} ) = f(x; z) + f(x;w) + f(y; z) + f(y;w)\]
and
\[f(x + y; z + w) + f(x + y; z - w) = 2f(x; z) + 2f(x;w) + 2f(y; z) + 2f(y;w)\]
in paranormed spaces.
710
718
Jae-Hyeong
Bae
Humanitas College
Kyung Hee University
Republic of Korea
jhbae@khu.ac.kr
Won-Gil
Park
Department of Mathematics Education, College of Education
Mokwon University
Republic of Korea
wgpark@mokwon.ac.kr
Cauchy-Jensen mapping
additive-quadratic mapping
paranormed space.
Article.23.pdf
[
[1]
Y. J. Cho, C. Park, Y. O. Yang, Stability of derivations in fuzzy normed algebras, J. Nonlinear Sci. Appl., 8 (2015), 1-7
##[2]
P. Găvruţa, A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl., 184 (1994), 431-436
##[3]
D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci., 27 (1941), 222-224
##[4]
C. Park, Additive \(\rho\)-functional inequalities, J. Nonlinear Sci. Appl., 7 (2014), 296-310
##[5]
C. Park, J. R. Lee, Functional equations and inequalities in paranormed spaces, J. Inequal. Appl., 2013 (2013), 1-23
##[6]
C. Park, J. R. Lee, Approximate ternary quadratic derivation on ternary Banach algebras and C*-ternary rings: revisited, J. Nonlinear Sci. Appl., 8 (2015), 218-223
##[7]
W. G. Park, J. H. Bae, On a Cauchy-Jensen functional equation and its stability, J. Math. Anal. Appl., 323 (2006), 634-643
##[8]
W. G. Park, J. H. Bae, B. H. Chung, On an additive-quadratic functional equation and its stability, J. Appl. Math. & Computing, 18 (2005), 563-572
##[9]
T. M. Rassias, On the stability of linear mappings in Banach spaces, Proc. Amer. Math. Soc., 72 (1978), 297-300
##[10]
S. M. Ulam, A Collection of Mathematical Problems, Interscience Publishers, New York (1960)
##[11]
A. Wilansky, Modern Methods in Topological Vector Space, McGraw-Hill International Book Co., New York (1978)
]
Fixed point results for various contractions in parametric and fuzzy b-metric spaces
Fixed point results for various contractions in parametric and fuzzy b-metric spaces
en
en
The notion of parametric metric spaces being a natural generalization of metric spaces was recently introduced and studied by Hussain et al. [A new approach to fixed point results in triangular intuitionistic
fuzzy metric spaces, Abstract and Applied Analysis, Vol. 2014, Article ID 69-139, 16 pp]. In this paper
we introduce the concept of parametric b-metric space and investigate the existence of fixed points under
various contractive conditions in such spaces. As applications, we derive some new fixed point results in
triangular partially ordered fuzzy b-metric spaces. Moreover, some examples are provided here to illustrate
the usability of the obtained results.
719
739
Nawab
Hussain
Department of Mathematics
King Abdulaziz University
Saudi Arabia
nhusain@kau.edu.sa
Peyman
Salimi
Young Researchers and Elite Club
Rasht Branch, Islamic Azad University
Iran
salimipeyman@gmail.com
Vahid
Parvaneh
Department of Mathematics
Gilan-E-Gharb Branch, Islamic Azad University
Iran
vahid.parvaneh@kiau.ac.ir
Fixed point theorem
fuzzy b-metric spaces
contractions.
Article.24.pdf
[
[1]
R. P. Agarwal, N. Hussain, M. A. Taoudi , Fixed point theorems in ordered Banach spaces and applications to nonlinear integral equations , Abstr. Appl. Anal., 2012 (2012), 1-15
##[2]
M. A. Alghamdi, N. Hussain, P. Salimi, Fixed point and coupled fixed point theorems on b-metric-like spaces, J. Inequal. Appl., 2013 (2013), 1-25
##[3]
I. Altun, D. Turkoglu, Some fixed point theorems on fuzzy metric spaces with implicit relations, Commun. Korean Math. Soc., 23 (2008), 111-124
##[4]
G. V. R. Babu, M. L. Sandhya, M. V. R. Kameswari, A note on a fixed point theorem of Berinde on weak contractions, Carpathian J. Math., 24 (2008), 8-12
##[5]
V. Berinde, General contrcactive fixed point theorems for Ćirić-type almost contraction in metric spaces, Carpathian J. Math., 24 (2008), 10-19
##[6]
L. Ćirić, M. Abbas, R. Saadati, N. Hussain, Common fixed points of almost generalized contractive mappings in ordered metric spaces, Appl. Math. Comput., 217 (2011), 5784-5789
##[7]
S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inf. Univ. Ostravensis, 1 (1993), 5-11
##[8]
S. Czerwik, Nonlinear set-valued contraction mappings in b-metric spaces, Atti Sem. Mat. Fis. Univ. Modena, 46 (1998), 263-276
##[9]
C. Di Bari, C. Vetro, A fixed point theorem for a family of mappings in a fuzzy metric space, Rend. Circ. Math. Palermo, 52 (2003), 315-321
##[10]
D. Dukić, Z. Kadelburg, S. Radenović, Fixed points of Geraghty-type mappings in various generalized metric spaces, Abstr. Appl. Anal., 2011 (2011), 1-13
##[11]
A. George, P. Veeramani , On some results in fuzzy metric spaces, Fuzzy Sets and Systems, 64 (1994), 395-399
##[12]
M. A. Geraghty, On contractive mappings , Proc. Amer. Math. Soc., 40 (1973), 604-608
##[13]
D. Gopal, M. Imdad, C. Vetro, M. Hasan, Fixed point theory for cyclic weak \(\phi\)-contraction in fuzzy metric space , J. Nonlinear Anal. Appl., 2012 (2012), 1-11
##[14]
M. Grabiec, Fixed points in fuzzy metric spaces, Fuzzy Sets and Systems, 27 (1988), 385-389
##[15]
N. Hussain, S. Al-Mezel, P. Salimi, Fixed points for \(\psi\)-graphic contractions with application to integral equations, Abstr. Appl. Anal., 2013 (2013), 1-11
##[16]
N. Hussain, S. Khaleghizadeh, P. Salimi, A. A. N. Abdou, A new approach to fixed point results in triangular intuitionistic fuzzy metric spaces, Abstr. Appl. Anal., 2014 (2014), 1-16
##[17]
N. Hussain, V. Parvaneh, J. R. Roshan, Z. Kadelburg, Fixed points of cyclic weakly (\( \psi,\varphi, L, A,B\))-contractive mappings in ordered b-metric spaces with applications, Fixed Point Theory Appl., 2013 (2013), 1-18
##[18]
N. Hussain, P. Salimi, Implicit contractive mappings in Modular metric and Fuzzy Metric Spaces, The Sci. World J., 2014 (2014), 1-13
##[19]
N. Hussain, M. H. Shah, KKM mappings in cone b-metric spaces, Comput. Math. Appl., 62 (2011), 1677-1684
##[20]
N. Hussain, M. A. Taoudi , Krasnosel'skii-type fixed point theorems with applications to Volterra integral equations, Fixed Point Theory Appl., 2013 (2013), 1-16
##[21]
M. A. Khamsi, N. Hussain, KKM mappings in metric type spaces, Nonlinear Anal., 73 (2010), 3123-3129
##[22]
M. S. Khan, M. Swaleh, S. Sessa, Fixed point theorems by altering distances between the points, Bull. Austral. Math. Soc., 30 (1984), 1-9
##[23]
M. A. Kutbi, J. Ahmad, A. Azam, N. Hussain, On fuzzy fixed points for fuzzy maps with generalized weak property, J. Appl. Math., 2014 (2014), 1-12
##[24]
J. J. Nieto, R. Rodríguez-López , Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order, 22 (2005), 223-229
##[25]
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 Appl., 2013 (2013), 1-23
##[26]
B. Schweizer, A. Sklar, Statistical metric spaces, Pacific J. Math., 10 (1960), 314-334
]
Some new Hermite--Hadamard type inequalities for geometrically quasi-convex functions on co-ordinates
Some new Hermite--Hadamard type inequalities for geometrically quasi-convex functions on co-ordinates
en
en
In the paper, the authors introduce a new concept ''geometrically quasi-convex function on co-ordinates''
and establish some new Hermite-Hadamard type inequalities for geometrically quasi-convex functions on
the co-ordinates.
740
749
Xu-Yang
Guo
College of Mathematics
Inner Mongolia University for Nationalities
China
guoxuyang1991@qq.com
Feng
Qi
Department of Mathematics
College of Science
China
qifeng618@gmail.com;qifeng618@hotmail.com
Bo-Yan
Xi
College of Mathematics
Inner Mongolia University for Nationalities
China
baoyintu78@qq.com
Geometrically quasi-convex function
Hermite-Hadamard type integral inequality
Hölder inequality.
Article.25.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, Some inequalities for \((s_1;m_1)-(s_2;m_2)\)-convex functions on co-ordinates, Glob. J. Math. Anal., 1 (2013), 22-28
##[3]
S. P. Bai, S. H. Wang, F. Qi , Some new integral inequalities of Hermite-Hadamard type for (\(\alpha;m; P\))-convex functions on co-ordinates, J. Appl. Anal. Comput., (2015), -
##[4]
S. S. Dragomir, On Hadamard's inequality for convex functions on the co-ordinates in a rectangle from the plane, Taiwanese J. Math., 5 (2001), 775-788
##[5]
S. S. Dragomir, C. E. M. Pearce, Selected Topics on Hermite-Hadamard Inequalities and Applications, RGMIA Monographs, Victoria University (2000)
##[6]
S. S. Dragomir, J. Pečarić, L. E. Persson, Some inequalities of Hadamard type, Soochow J. Math., 21 (1995), 335-341
##[7]
M. A. Latif, S. S. Dragomir , On some new inequalities for differentiable co-ordinated convex functions, J. Inequal. Appl., 2012 (2012), 1-13
##[8]
M. E. Özdemir, A. O. Akdemir, H. Kavurmaci, M. Avci, On the Simpson's inequality for co-ordinated convex functions, arXive, (2010), 1-8
##[9]
M. E. Özdemir, A. O. Akdemir, Ç . Yıldız, On co-ordinated quasi-convex functions, Czechoslovak Math. J., 62 (2012), 889-900
##[10]
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
##[11]
B. Y. Xi, R.-F. Bai, F. Qi , Hermite-Hadamard type inequalities for the m- and (\(\alpha;m\))-geometrically convex functions, Aequationes Math., 84 (2012), 261-269
##[12]
B. Y. Xi, S. P. Bai, F. Qi , Some new inequalities of Hermite-Hadamard type for (\(\alpha;m_1)-(s;m_2\))-convex functions on co-ordinates, Research Gate, ()
##[13]
B. Y. Xi, J. Hua, F. Qi , Hermite-Hadamard type inequalities for extended s-convex functions on the co-ordinates in a rectangle, J. Appl. Anal., 20 (2014), 29-39
##[14]
B. Y. Xi, F. Qi, Some Hermite-Hadamard type inequalities for differentiable convex functions and applications, Hacet. J. Math. Stat., 42 (2013), 243-257
##[15]
B. Y. Xi, F. Qi , Some integral inequalities of Hermite-Hadamard type for convex functions with applications to means, J. Funct. Spaces Appl., 2012 (2012), 1-14
]
Tripled fixed point theorems in cone metric spaces under \(F\)-invariant set and \(c\)-distance
Tripled fixed point theorems in cone metric spaces under \(F\)-invariant set and \(c\)-distance
en
en
The concept of cone metric spaces has been introduced recently as a generalization of metric spaces. The
aim of this paper is to give the definitions of \(F\)-invariant sets denoted by \(M\) in case of \(M \in X^6\) in cone and
ordered cone version. we also establish some tripled fixed point theorems in cone metric spaces under the
concept of an \(F\)-invariant set for mappings \(F : X^3 \rightarrow X\) and \(c\)-distance on the one hand, and in partially
ordered cone metric spaces under the same concepts on the other hand. The present theorems expand and
generalize several well-known comparable results in literature in cone metric spaces and ordered cone metric
spaces,respectively. An interesting example is given to support our results.
750
762
Sahar Mohammad
Abusalim
School of Mathematical Sciences, Faculty of Science and Technology
Malaysia
saharabosalem@gmail.com
Mohd Salmi Md
Noorani
School of Mathematical Sciences, Faculty of Science and Technology
Universiti Kebangsaan Malaysia, 43600 UKM Bangi
Malaysia
msn@ukm.my
Cone metric spaces
partially ordered cone metric spaces
tripled fixed points
c-distance
F-invariant set.
Article.26.pdf
[
[1]
M. Abbas, G. Jungck , Common fixed point results for noncommuting mappings without continuity in cone metric space, J. Math. Anal. Appl., 341 (2008), 416-420
##[2]
M. Abbas, A. R. Khan, T. Nazir , Coupled common fixed point result in two generalized metric spaces, Appl. Math. Compt., 217 (2011), 6328-6336
##[3]
M. Abbas, M. A. Khan, S. Radenović, Common coupled fixed point theorems in cone metric spaces for w-compatible mappings, Appl. Math. Comput., 217 (2010), 195-202
##[4]
A. G. B. Ahmad, Z. M. Fadail, M. Abbas, Z. Kadelburg, S. Radenović , Some fixed and periodic points in abstract metric spaces, Abstr. Appl. Anal., 2012 (2012), 1-15
##[5]
S. Abusalim, M. S. M. Noorani , Generalized Distance in Cone Metric Spaces and Tripled Coincidence Point and Common Tripled Fixed Point Theorems, Far East J. Math. Sci., 91 (2014), 65-87
##[6]
H. Aydi, M. Abbas, W. Sintunavarat, P. Kumam, Tripled fixed point of W-compatible mappings in abstract metric spaces, Fixed Point Theory Appl., 2012 (2012), 1-20
##[7]
V. Berinde, M. Borcut , Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces, Nonlinear Anal., 74 (2011), 4889-4897
##[8]
T. G. Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal., 65 (2006), 1379-1393
##[9]
M. Borcut , Tripled coincidence theorems for contractive type mappings in partially ordered metric spaces, Appl. Math. Comput, 218 (2012), 7339-7346
##[10]
M. Borcut, V. Berinde, Tripled coincidence theorems for contractive type mappings in partially ordered metric spaces, Appl. Math. Comput., 218 (2012), 5929-5936
##[11]
M. Borcut, M. Pacurar, V. Berinde, Tripled Fixed Point Theorems for Mixed Monotone Kannan Type Contractive Mappings, J. Appl. Math., 2014 (2014), 1-8
##[12]
Y. J. Cho, G. He, N. J. Huang, The existence results of coupled quasi-solutions for a class of operator equations, Bull. Korean Math. Soc., 47 (2010), 455-465
##[13]
Y. J. Cho, Z. Kadelburg, R. Saadati, W. Shatanawi , Coupled Fixed Point Theorems under Weak Contractions, Discrete Dyn. Nat. Soc., 2012 (2012), 1-9
##[14]
Y. J. Cho, R. Saadati, S. Wang, Common Fixed Point Theorems on Generalized Distance in Ordered Cone Metric Spaces, Comput. Math. Appl., 61 (2011), 1254-1260
##[15]
M. DJ ordj ević, D. DJ orić, Z. Kadelburg, S. Radenović, D. Spasić, Fixed point results under c-distance in tvs-cone metric spaces, Fixed Point Theory Appl., 2011 (2011), 1-9
##[16]
Z. M. Fadail, A. G. B. Ahmad, Common coupled fixed point theorems of single-valued mapping for c-distance in cone metric spaces, Abstr. Appl. Anal., 2012 (2012), 1-24
##[17]
Z. M. Fadail, A. G. B. Ahmad, Coupled fixed point theorems of single-valued mapping for c-distance in cone metric spaces, J. Appl. Math., 2012 (2012), 1-20
##[18]
Z. M. Fadail, A. G. B. Ahmad, Z. Golubović, Fixed point theorems of single-valued mapping for c-distance in cone metric spaces, Abstr. Appl. Anal., 2012 (2012), 1-11
##[19]
Z. M. Fadail, A. G. B. Ahmad, L. Paunović, New fixed point results of single-valued mapping for c-distance in cone metric spaces, Abstr. Appl. Anal., 2012 (2012), 1-12
##[20]
M. E. Gordji, Y. J. Cho, H. Baghani, Coupled fixed point theorems for contractions in intuitionistic fuzzy normed spaces, Math. Comput. Modelling, 54 (2011), 1897-1906
##[21]
L. G. Huang, X. Zhang, Cone Metric Spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl., 332 (2207), 1468-1476
##[22]
G. Jungck, S. Radenović, S. Radojević, V. Rakočević, Common fixed point theorems for weakly compatible pairs on cone metric spaces, Fixed Point Theory Appl., 2009 (2009), 1-13
##[23]
O. Kada, T. Suzuki, W. Takahashi, Nonconvex Minimization Theorems And Fixed Point Theorems In Complete Metric Spaces, Math. Japon., 44 (1996), 381-391
##[24]
L. V. Kantorovich, The majorant principle and Newton's method, Dokl. Akad. Nauk SSSR (N.S.), 76 (1951), 17-20
##[25]
E. Karapinar, Couple fixed point theorems for nonlinear contractions in cone metric spaces, Comput. Math. Appl., 59 (2010), 3656-3668
##[26]
E. Karapinar, Tripled fixed point theorems in partially ordered metric spaces, Stud. Univ. Babes-Bolyai Maths., 58 (2013), 75-85
##[27]
E. Karapinar, P. Kumam, W. Sintunavarat, Coupled fixed point theorems in cone metric spaces with a c-distance and applications, Fixed Point Theory Appl., 2012 (2012), 1-19
##[28]
V. Lakshmikantham, L. Ćirić , Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Anal., 70 (2009), 4341-4349
##[29]
N. V. Luong, N. X. Thuan, Coupled fixed points in partially ordered metric spaces, Bull. Math. Anal. Appl., 2 (2010), 16-24
##[30]
P. P. Murthy, Triple common fixed point theorem for w-compatible mapping in ordered cone metric spaces, Adv. Fixed Point Theory, 2 (2012), 157-175
##[31]
H. K. Nashine, Z. Kadelburg, S. Radenović, Coupled common fixed point theorems for \(w^*\)-compatible mappingsin in ordered cone metric spaces, Appl. Math. Comput., 218 (2012), 5422-5432
##[32]
S. H. Rezapour, R. Hamlbarani , Some note on the paper ''cone metric spaces and fixed point theorems of contractive mappings'', J. Math. Anal. Appl., 345 (2008), 719-724
##[33]
F. Sabetghadam, H. P. Masiha, A. H. Sanatpour, Some coupled fixed point theorems in cone metric space, Fixed Point Theory Appl., 2009 (2009), 1-8
##[34]
B. Samet, C. Vetro, Coupled fixed point, F-invariant set and fixed point of N-order, Ann. Funct. Anal., 1 (2010), 46-56
##[35]
W. Shatanawi , Some common coupled fixed point results in cone metric spaces, Int. J. Math. Anal., 4 (2010), 2381-2388
##[36]
W. Shatanawi, M. Abbas, T. Nazir, Common coupled fixed point results in two generalized metric spaces, fixed point theory appl., 2011 (2011), 1-13
##[37]
W. Shatanawi, E. Karapinar, H. Aydi , Coupled coincidence points in partially ordered cone metric spaces with c-distance, J. Appl Math., 2012 (2012), 1-15
##[38]
W. Sintunavarat, Y. J. Cho, P. Kumam, Common Fixed Point Theorems for c-distance in Ordered Cone Metric Spaces, Comput. Math. Appl., 62 (2011), 1969-1978
##[39]
W. Sintunavarat, Y. J. Cho, P. Kumam, Coupled coincidence point theorems for contractions without commutative condition in intuitionistic fuzzy normed spaces, fixed point theory appl., 2011 (2011), 1-13
##[40]
W. Sintunavarat, Y. J. Cho, P. Kumam, Coupled fixed point theorems for weak contraction mapping under F- invariant set, Abstr. Appl. Anal., 2012 (2012), 1-15
##[41]
J. S. Vandergraft, Newton method for convex operators in partially ordered spaces, SIAM J. Numer. Anal., 4 (1967), 406-432
##[42]
S. Wang, B. Guo, Distance in Cone Metric Spaces and common fixed point theorems, Appl. Math Lett., 24 (2011), 1735-1739
##[43]
P. P. Zabreĭko, K-metric and K-normed spaces: survey, Collect. Math., 48 (1997), 825-859
]
A model of the groundwater flowing within a leaky aquifer using the concept of local variable order derivative
A model of the groundwater flowing within a leaky aquifer using the concept of local variable order derivative
en
en
One of the big problems we encounter in groundwater modeling is to provide a correct model that can be
used to describe the movement of water via a particular geological formation. In this work, in order to
further enhance the model of groundwater
flow in a leaky aquifer, we made use of a new derivative called
the local variable order derivative. The derivative includes into mathematical formula the complexity of the
leaky aquifer, which is for instance the variation of the aquifer, or the heterogeneity of the leaky aquifer.
The modified equation was solved using the concept of iterative method. We presented in detail the stability
and the uniqueness of the special solution.
763
775
Abdon
Atangana
Institute for groundwater Studies, Faculty of Natural and Agricultural Sciences
University of the Free State
South Africa
abdonatangana@yahoo.fr
Emile Franc Doungmo
Goufo
Department of Mathematical Sciences
University of South Africa
003 South Africa
franckemile2006@yahoo.ca
Leaky aquifer
variable order derivative
stability and uniqueness analysis
special solution.
Article.27.pdf
[
[1]
A. Atangana , Drawdown in prolate spheroidal-spherical coordinates obtained via Green's function and perturbation methods, Commun. Nonlinear Sci. Num. Simul., 19 (2014), 1259-1269
##[2]
A. Atangana, Analytical solutions for the recovery tests after constant-discharge tests in confined aquifers, Water SA, 40 (2014), 595-600
##[3]
A. Atangana, B. Necdet, The use of fractional order derivative to predict the groundwater flow , Math. Probl. Eng., 2013 (2013), 1-9
##[4]
J. B. Brackenridge, The key to Newton's dynamics. The Kepler problem and the Principia, University of California Press, Berkeley (1995)
##[5]
M. A. B. Deakin, The development of the Laplace transform, Arch. Hist. Exact Sci., 26 (1982), 351-381
##[6]
M. A. B. Deakin, The development of the Laplace transform , Arch. Hist. Exact Sci., 25 (1981), 343-390
##[7]
E. F. Doungmo Goufo, A mathematical analysis of fractional fragmentation dynamics with growth, J. Funct. Spaces, 2014 (2014), 1-7
##[8]
E. F. Doungmo Goufo, A biomathematical view on the fractional dynamics of cellulose degradation, Fract. Cal. Appl. Anal., (in press), -
##[9]
E. F. Doungmo Goufo, R. Maritz, J. Munganga, Some properties of Kermack-McKendrick epidemic model with fractional derivative and nonlinear incidence, Adv. Difference Equ., 2014 (2014), 1-9
##[10]
V. J. Katz, A History of Mathematics: An Introduction, Harper Collins, New York (1993)
##[11]
G. W. F. V. Leibniz, C. I. Gerhardt, The Early Mathematical Manuscripts of Leibniz, Open Court Publishing, Chicago (1920)
##[12]
I. Newton, Sir Isaac Newton's Mathematical Principles of Natural Philosophy and His System of the World, tr. A. Motte, rev. Florian Cajori. University of California Press, Berkeley (1934)
##[13]
H. J. Ramey, Well loss function and the skin effect: A review, In: Narasimhan TN (ed.) Recent Trends in Hydrogeology, Geo. Soc. Amer. Special paper, 189 (1982), 265-272
##[14]
C. V. Theis, The relation between the lowering of the Piezometric surface and the rate and duration of discharge of well using ground-water storage, Trans, Amer. Geophys. Union, 16 (1935), 519-524
]
Stability of functional inequalities associated with the Cauchy-Jensen additive functional equalities in non-Archimedean Banach spaces
Stability of functional inequalities associated with the Cauchy-Jensen additive functional equalities in non-Archimedean Banach spaces
en
en
In this article, we prove the generalized Hyers-Ulam stability of the following Pexider functional inequalities
\[\|f(x) + g(y) + kh(z)\| \leq \| kp (\frac{ x + y}{ k} + z)\|,\]
\[\|f(x) + g(y) + h(z)\| \leq \| kp (\frac{ x + y+z}{ k} )\|,\]
in non-Archimedean Banach spaces.
776
786
Sang Og
Kim
Department of Mathematics
Hallym University
Korea
sokim@hallym.ac.kr
Abasalt
Bodaghi
Department of Mathematics
Garmsar Branch, Islamic Azad University
Iran
abasalt.bodaghi@gmail.com
Choonkil
Park
Department of Mathematics, Research Institute for Natural Sciences
Hanyang University
Korea
baak@hanyang.ac.kr
Hyers-Ulam stability
Pexider Cauchy-Jensen functional inequality
non-Archimedean space
additive mapping.
Article.28.pdf
[
[1]
T. Aoki , On the stability of the linear transformation mappings in Banach spaces, J. Math. Soc. Japan, 2 (1950), 64-66
##[2]
Y. Cho, C. Park, R. Saadati , Functional inequalities in non-Archimedean Banach spaces, Appl. Math. Lett., 23 (2010), 1239-1242
##[3]
S. Czerwik, Functional Equations and Inequalities in Several Variables, World Scientific Publishing, NJ (2002)
##[4]
W. Fechner , Stability of functional inequalities associated with the Jordan-von Neumann functional equations, Aequationes Math., 71 (2006), 149-161
##[5]
G. L. Forti, An existence and stability theorem for a class of functional equations, Stochastica, 4 (1980), 23-30
##[6]
P. Găvruţa, A generalization of the Hyers-Ulam-Rassias stability of approximate additive mappings, J. Math. Anal. Appl., 184 (1994), 431-436
##[7]
A. Gilányi, Eine zur Parallelogrammgleichung äquivalente Ungleichung, Aequationes Math., 62 (2001), 303-309
##[8]
A. Gilányi , On a problem by K. Nikodem, Math. Inequal. Appl., 5 (2002), 707-710
##[9]
D. H. Hyers, On the stability of linear functional equations, Proc. Nat. Acad. Sci. USA., 27 (1941), 222-224
##[10]
D. H. Hyers, G. Isac,T. M. Rassias , Stability of Functional Equations in Several Variables, Birkhäuser, Boston (1998)
##[11]
S. M. Jung , Hyers-Ulam-Rassias Stability of Functional Equations in Mathematical Analysis, Springer, New York (2011)
##[12]
G. Lu, C. Park, Additive functional inequalities in Banach spaces, J. Inequal. Appl., 2012 (2012), 1-10
##[13]
C. Park, Y. Cho, M. Han, Functional inequalities associated with Jordan-von Neumann-type additive functional equations, J. Inequal. Appl., 2007 (2007), 1-13
##[14]
Th. M. Rassias, On the stability of linear mappings in Banach spaces, Proc. Amer. Math. Soc., 72 (1978), 297-300
##[15]
J. Rätz, On inequalities associated with the Jordan-von Neumann functional equation, Aequationes Math., 66 (2003), 191-200
##[16]
S. M. Ulam, Problems of modern mathematics, Sciences Editions John Wiley & Sons Inc., New York (1960)
]
Common fixed point theorems of generalized Lipschitz mappings in cone b-metric spaces over Banach algebras and applications
Common fixed point theorems of generalized Lipschitz mappings in cone b-metric spaces over Banach algebras and applications
en
en
In this paper, we introduce the concept of cone b-metric space over Banach algebra and present some common
fixed point theorems in such spaces. Moreover, we support our results by two examples. In addition, some
applications in the solutions of several equations are given to illustrate the usability of the obtained results.
787
799
Huaping
Huang
School of Mathematics and Statistics
Hubei Normal University
China
mathhhp@163.com
Stojan
Radenović
Faculty of Mathematics and Information Technology
Dong Thap University
Viet Nam
radens@beotel.net
Generalized Lipschitz constant
cone b-metric space over Banach algebra
c-sequence
weakly compatible.
Article.29.pdf
[
[1]
M. Abbas, G. Jungck, Common fixed point results for noncommuting mappings without continuity in cone metric spaces, J. Math. Anal. Appl., 341 (2008), 416-420
##[2]
S. M. Abusalim, M. S. M. Noorani , Fixed point and common fixed point theorems on ordered cone b-metric spaces, Abstr. Appl. Anal., 2013 (2013), 1-7
##[3]
A. Azam, N. Mehmood, J. Ahmad, S. Radenović, Multivalued fixed point theorems in cone b-metric spaces, Fixed Point Theory Appl., 2013 (2013), 1-9
##[4]
W. S. Du , A note on cone metric fixed point theory and its equivalence, Nonlinear Anal., 72 (2010), 2259-2261
##[5]
W. S. Du, E. Karapiniar, A note on cone b-metric and its related results: generalizations or equivalence, Fixed Point Theory Appl., 2013 (2013), 1-7
##[6]
Z. Ercan, On the end of the cone metric spaces, Topology Appl., 166 (2014), 10-14
##[7]
Y. Feng, W. Mao, The equivalence of cone metric spaces and metric spaces, Fixed Point Theory, 11 (2010), 259-263
##[8]
H. Huang, S. Xu, Fixed point theorems of contractive mappings in cone b-metric spaces and applications, Fixed Point Theory Appl., 2013 (2013), 1-10
##[9]
L. Huang, X. Zhang , Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl., 332 (2007), 1468-1476
##[10]
N. Hussian, M. H. Shah, KKM mappings in cone b-metric spaces, Comput. Math. Appl., 62 (2011), 1677-1684
##[11]
S. Janković, Z. Kadelburg, S. Radenović , On cone metric spaces: A survey, Nonlinear Anal., 74 (2011), 2591-2601
##[12]
Z. Kadelburg, S. Radenović, A note on various types of cones and fixed point results in cone metric spaces, Asian J. Math. Appl., 2013 (2013), 1-7
##[13]
Z. Kadelburg, S. Radenović, V. Rakočević, A note on the equivalence of some metric and cone metric fixed point results, Appl. Math. Lett., 24 (2011), 370-374
##[14]
P. Kumam, N. V. Dung, V. T. L. Hang , Some equivalence between cone b-metric spaces and b-metric spaces, Abstr. Appl. Anal., 2013 (2013), 1-8
##[15]
Z. Li, S. Jiang , Quasi-contractions restricted with linear bounded mappings in cone metric spaces, Fixed Point Theory Appl., 2014 (2014), 1-10
##[16]
H. Liu, S. Xu, Cone metric spaces with Banach algebras and fixed point theorems of generalized Lipschitz mappings, Fixed Point Theory Appl., 2013 (2013), 1-10
##[17]
X. Pai, S. Liu, H. Jiao, Some new coincidence and common fixed point theorems in cone metric spaces, Afr. Math., 24 (2013), 135-144
##[18]
S. Radenović, S. Simić, N. Cakić, Z. Golubović, A note on tvs-cone metric fixed point theory, Math. Comput. Model., 54 (2011), 2418-2422
##[19]
W. Rudin, Functional Analysis, McGraw-Hill, New York (1991)
##[20]
G. Song, X. Sun, Y. Zhao, G. Wang, New common fixed point theorems for maps on cone metric spaces, Appl. Math. Lett., 23 (2010), 1033-1037
##[21]
S. Xu, S. Radenović, Fixed point theorems of generalized Lipschitz mappings on cone metric spaces over Banach algebras without assumption of normality, Fixed Point Theory Appl., 2014 (2014), 1-12
]
On some new fixed point results for rational Geraghty contractive mappings in ordered b-metric spaces
On some new fixed point results for rational Geraghty contractive mappings in ordered b-metric spaces
en
en
In this paper we prove some new fixed point results in the context of ordered b-metric spaces for rational
Geraghty contractive mappings. Thus our results in the new context generalize, extend, unify, enrich and
complement fixed point theorems of contractive mappings in several aspects. One example is given to show
the validity of our results. In addition, we obtain the periodic property of these mappings.
800
807
Stojan
Huang
School of Mathematics and Statistics
Hubei Normal University
China
mathhhp@163.com
Ljiljana
Paunović
Teacher Education School in Prizren-Leposavić
Serbia
ljiljana.paunovic@gmail.com
Huaping
Radenović
Faculty of Mathematics and Information Technology
Dong Thap University
Viêt Nam
radens@beotel.net
Fixed point
b-metric space
rational Geraghty contraction
ordered b-metric space.
Article.30.pdf
[
[1]
M. Abbas, V. Parvaneh, A. Razani, Periodic points of T-Ćirić generalized contraction mappings in ordered metric spaces, Georgian Math. J., 19 (2012), 597-610
##[2]
A. G. B. Ahmad, Z. M. Fadail, M. Abbas, Z. Kadelburg, S. Radenović, Some fixed and periodic points in abstract metric spaces, Abstr. Appl. Anal., 2012 (2012), 1-15
##[3]
A. Aghajani, M. Abbas, J. Roshan , Common fixed point of generalized weak contractive mappings in partially ordered b-metric spaces, Math. Slovaca, 4 (2014), 941-960
##[4]
A. Azam, B. Fisher, M. Khan, Common fixed point theorems in complex valued metric spaces, Numer. Funct. Anal. Optim., 32 (2011), 243-253
##[5]
S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fundam. Math., 3 (1922), 133-181
##[6]
S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostraviensis, 1 (1993), 5-11
##[7]
D. Ðukić, Z. Kadelburg, S. Radenović, Fixed points of Geraghty-type mappings in various generalized metric spaces, Abstr. Appl. Anal., 2011 (2011), 1-13
##[8]
M. A. Geraghty, On contractive mappings, Proc. Am. Math. Soc., 40 (1973), 604-608
##[9]
N. Hussain, D. Ðorić, Z. Kadelburg, S. Radenović, Suzuki-type fixed point results in metric type spaces, Fixed Point Theory Appl., 2012 (2012), 1-12
##[10]
D. S. Jaggi , Some unique fixed point theorems, Indian J. Pure Appl. Math., 8 (1977), 223-230
##[11]
G. S. Jeong, B. E. Rhoades, Maps for which \(F (T) = F (T^n)\) , Fixed Point Theory Appl., 6 (2005), 71-131
##[12]
M. Jovanović, Z. Kadelburg, S. Radenović , Common fixed point results in metric-type spaces, Fixed Point Theory Appl., 2010 (2010), 1-15
##[13]
M. Khamsi, Remarks on cone metric spaces and fixed point theorems of contractive mappings, Fixed Point Theory Appl., 2010 (2010), 1-7
##[14]
H. K. Nashine, M. Imdad, M. Hasan, Common fixed point theorems under rational contractions in complex valued metric spaces, J. Nonlinear Sci. Appl., 7 (2014), 42-50
##[15]
J. J. Nieto, R. Rodríguez-López, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order, 22 (2005), 223-239
##[16]
J. J. Nieto, R. Rodríguez-López, Existence and uniqueness of fixed points in partially ordered sets and applications to ordinary differential equations, Acta Math. Sin., Engl. Ser., 23 (2007), 2205-2212
##[17]
V. Parvaneh, J. Roshan, S. Radenović, Existence of tripled coincidence points in ordered b-metric spaces and an application to a system of integral equations , Fixed Point Theory Appl., 2013 (2013), 1-19
##[18]
A. C. M. Ran, M. C. B. Reurings, C. B. Martine, A fixed point theorem in partially ordered sets and some application to matrix equations , Proc. Am. Math. Soc., 132 (2004), 1435-1443
##[19]
J. R. Roshan, V. Parvaneh, N. Shobkolaei, S. Sedghi, W. Shatanawi , Common fixed points of almost generalized \((\psi,\varphi )_s\)-contractive mappings in ordered b-metric spaces, Fixed Point Theory Appl., 2013 (2013), 1-23
##[20]
J. R. Roshan, V. Parvaneh, Z. Kadelburg , Common fixed point theorems for weakly isotone increasing mappings in ordered b-metric spaces, J. Nonlinear Sci. Appl., 7 (2014), 229-245
##[21]
R. J. Shahkoohi, A. Razani , Some fixed point theorems for rational Geraghty contractive mappings in ordered b-metric spaces, J. Inequal. Appl., 2014 (2014), 1-23
]
A note on common fixed point theorems for isotone increasing mappings in ordered b-metric spaces
A note on common fixed point theorems for isotone increasing mappings in ordered b-metric spaces
en
en
In this article we prove the existence of common fixed points for isotone increasing mappings in ordered b-metric
spaces. Our results unite and improve the recent remarkable results, established by Roshan et al. [J.
R. Roshan, V. Parvaneh, Z. Kadelburg, J. Nonlinear Sci. Appl. 7 (2014), 229–245], with much more general
conditions and shorter proofs. An example is given to show the superiority of our genuine generalization.
808
815
Huaping
Huang
School of Mathematics and Statistics
Hubei Normal University
China
mathhhp@163.com
Jelena
Vujaković
Faculty of Sciences and Mathematics
Serbia
enav@ptt.rs
Stojan
Radenović
Faculty of Mathematics and Information Technology
Dong Thap University
Viêt Nam
radens@beotel.net
Common fixed point
b-metric space
g-weakly isotone increasing
well ordered.
Article.31.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]
A. A. Harandi , Fixed point theory for quasi-contraction maps in b-metric spaces , Fixed Point Theory, 15 (2014), 351-358
##[3]
I. A. Bakhtin, The contraction principle in quasi metric spaces, Funct. Anal. Unianowsk Gos. Ped. Inst., 30 (1989), 26-37
##[4]
S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales , Fundam. Math., 3 (1922), 133-181
##[5]
S. Czerwik, Contraction mappings in b-metric spaces , Acta Math. Inform. Univ. Ostrav., 1 (1993), 5-11
##[6]
N. Hussain, D. Ðorić, Z. Kadelburg, S. Radenović, Suzuki-type fixed point results in metric type spaces , Fixed Point Theory Appl., 2012 (2012), 1-12
##[7]
N. Hussain, V. Parvaneh, J. R. Roshan, Z. Kadelburg , Fixed points of cyclic \((\psi,\varphi , L, A,B)\)- contractive mappings in ordered b-metric spaces with applications, Fixed Point Theory Appl., 2013 (2013), 1-18
##[8]
M. Jovanović, Z. Kadelburg, S. Radenović, Common fixed point results in metric-type spaces , Fixed Point Theory Appl., 2010 (2010), 1-15
##[9]
M. A. Khamsi, N. Hussain, KKM mappings in metric type spaces, Nonlinear Anal., 73 (2010), 3123-3129
##[10]
M. Kir, H. Kiziltunc, On some well known fixed point theorems in b-metric spaces, Turkish J. Anal. Number Theory, 1 (2013), 13-16
##[11]
J. J. Nieto, R. Rodríguez-López, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order, 22 (2005), 223-239
##[12]
J. J. Nieto, R. Rodríguez-López, Existence and uniqueness of fixed points in partially ordered sets and applications to ordinary differential equations, Acta Math. Sin., Engl. Ser., 23 (2007), 2205-2212
##[13]
V. Parvaneh, J. R. Roshan, S. Radenović, Existence of tripled coincidence points in ordered b-metric spaces and an application to a system of integral equations, Fixed Point Theory Appl., 2013 (2013), 1-19
##[14]
S. Radenović, Z. Kadelburg, Quasi-contractions on symmetric and cone symmetric spaces , Banach J. Math. Anal., 5 (2011), 38-50
##[15]
A. C. M. Ran, M. C. B. Reurings, C. B. Martine, A fixed point theorem in partially ordered sets and some application to matrix equations, Proc. Am. Math. Soc., 132 (2004), 1435-1443
##[16]
J. R. Roshan, V. Parvaneh, Z. Kadelburg , Common fixed point theorems for weakly isotone increasing mappings in ordered b-metric spaces, J. Nonlinear Sci. Appl., 7 (2014), 229-245
##[17]
J. R. Roshan, V. Parvaneh, N. Shobkolaei, S. Sedghi, W. Shatanawi, Common fixed points of almost generalized \((\psi,\varphi )_s\)-contractive mappings in ordered b-metric spaces, Fixed Point Theory Appl., 2013 (2013), 1-23
##[18]
M. P. Stanić, A. S. Cvetkovic, S. Simic, S. Dimitrijevic , Common fixed point under contractive condition of Ciric’s type on cone metric type spaces, Fixed Point Theory Appl., 2012 (2012), 1-7
]
Normed proper quasilinear spaces
Normed proper quasilinear spaces
en
en
The fundamental deficiency in the theory of quasilinear spaces, introduced by Aseev [S. M. Aseev, Trudy Mat.
Inst. Steklov., 167 (1985), 25–52], is the lack of a satisfactory definition of linear dependence-independence
and basis notions. Perhaps, this is the most important obstacle in the progress of normed quasilinear
spaces. In this work, after giving the notions of quasilinear dependence-independence and basis presented
by Banazılı[H. K. Banazılı, M.Sc. Thesis, Malatya, Turkey (2014)] and Çakan [S. Çakan, Ph.D. Seminar,
Malatya, Turkey (2012)], we introduce the concepts of regular and singular dimension of a quasilinear space.
Also, we present a new notion namely "proper quasilinear spaces" and show that these two kind dimensions
are equivalent in proper quasilinear spaces. Moreover, we try to explore some properties of finite regular
and singular dimensional normed quasilinear spaces. We also obtain some results about the advantages of
features of proper quasilinear spaces.
816
836
Sümeyye
Çakan
Department of Mathematics
Inönü University
Turkey
sumeyye.tay@gmail.com
Yılmaz
Yılmaz
Department of Mathematics
Inönü University
Turkey
yyilmaz44@gmail.com
Quasilinear spaces
Hausdorff metric
regular dimension
singular dimension
floor of an element
proper sets
proper quasilinear spaces.
Article.32.pdf
[
[1]
G. Alefeld, G. Mayer, Interval Analysis: theory and applications, J. Comput. Appl. Math., 121 (2000), 421-464
##[2]
S. M. Aseev, Quasilinear operators and their application in the theory of multivalued mappings, Trudy Mat. Inst. Steklov., 167 (1985), 25-52
##[3]
J. P. Aubin, H. Frankowska , Set-Valued Analysis, Birkhauser, Boston (1990)
##[4]
H. K. Banazılı , On Quasi linear Operators Between Quasilinear Spaces, M. Sc. Thesis, Malatya, Turkey (2014)
##[5]
H. Bozkurt, S. Çakan, Y. Yılmaz, Quasilinear Inner Product Spaces and Hilbert Quasilinear Spaces, Int. J. Anal., 2014 (2014), 1-7
##[6]
S. Çakan , Basis in Quasilinear Spaces, Ph.D. Seminar, Malatya, Turkey (2012)
##[7]
S. Çakan, Y. Yılmaz, Lower and Upper Semi Basis in Quasilinear Spaces , Erciyes Univer. J. Inst. Sci. Techn., 31 (2014), 97-104
##[8]
S. Çakan, Y. Yılmaz, On the Quasimodules and Normed Quasimodules, Nonlinear Func. Anal. Appl., (Accepted)
##[9]
E. Kreyszig , Introductory Functional Analysis with Applications, John Wiley-Sons Inc., New York (1989)
##[10]
V. Lakshmikantham, T. G. Bhaskar, J. Vasundhara Devi, Theory of set differential equations in metric spaces, Cambridge Scientific Publishers, Cambridge (2006)
##[11]
Y. Yılmaz, S. Çakan, S. Aytekin, Topological Quasilinear Spaces, Abstr. Appl. Anal., 2012 (2012), 1-10
]
Solving nonlinear \(\phi\) -strongly accretive operator equations by a one-step-two-mappings iterative scheme
Solving nonlinear \(\phi\) -strongly accretive operator equations by a one-step-two-mappings iterative scheme
en
en
A solution of nonlinear \(\phi\)-strongly accretive operator equations is found in this paper by using a one-step-
two-mappings iterative scheme in arbitrary real Banach spaces. We give an example to validate our main
theorem. Our results are different from those of Khan et. al., [S. H. Khan, A. Rafiq, N. Hussain, Fixed
Point Theory Appl., 2012 (2012), 10 pages] in view of different and independent iterative schemes in the
sense that none reduces to the other but extend and improve the results of Ding [X. P. Ding, Computers
Math. Appl., 33 (1997), 75-82] and many others.
837
846
Safeer Hussain
Khan
Department of Mathematics, Statistics and Physics
Qatar University
Qatar
safeer@qu.edu.qa
Birol
Gunduz
Department of Mathematics, Faculty of Science and Art
Erzincan University
Turkey
birolgndz@gmail.com
Sezgin
Akbulut
Department of Mathematics, Faculty of Science
Ataturk University
Turkey
sezginakbulut@atauni.edu.tr
One-step-two-mappings iterative scheme
\(\phi\)-strongly accretive operator
\(\phi\)-hemicontractive operator.
Article.33.pdf
[
[1]
C. E. Chidume , Iterative approximation of fixed points of Lipschitz strictly pseudo-contractive mappings, Proc. Amer. Math. Soc., 99 (1987), 283-288
##[2]
C. E. Chidume, M. O. Osilike, Fixed point iterations for strictly hemicontractive maps in uniformly smooth Banach spaces, Numer. Funct. Anal. Optimiz., 15 (1994), 779-790
##[3]
C. E. Chidume, M. O. Osilike, Nonlinear accretive and pseudo-contractive operator equations in Banach spaces, Nonlinear Anal., 31 (1998), 779-789
##[4]
R. Chugh, V. Kumar, Convergence of SP iterative scheme with mixed errors for accretive Lipschitzian and strongly accretive Lipschitzian operators in Banach space, Int. J. Comput. Math., 90 (2013), 1865-1880
##[5]
X. P. Ding, Iterative process with errors to nonlinear \(\phi\)-strongly accretive operator equations in arbitrary Banach spaces, Comput. Math. Appl., 33 (1997), 75-82
##[6]
N. Gurudwan, B. K. Sharma, Approximating solutions for the system of \(\phi\)-strongly accretive operator equations in reflexive Banach space, Bull. Math. Anal. Appl., 2 (2010), 32-39
##[7]
S. Kamimura, S. H. Khan, W. Takahashi, Iterative schemes for approximating solutions of relations involving accretive operators in Banach spaces, Fixed Point Theory Appl., 5 (2003), 41-52
##[8]
T. Kato , Nonlinear semigroups and evolution equations, J. Math. Soc. Japan., 19 (1967), 508-520
##[9]
S. H. Khan, N. Hussain , Convergence theorems for nonself-asymptotically nonexpansive mappings, Comput. Math. Appl., 55 (2008), 2544-2553
##[10]
A. R. Khan, V. Kumar, N. Hussain, Analytical and Numerical Treatment of Jungck-Type Iterative Schemes, Appl. Math. Comput., 231 (2014), 521-535
##[11]
S. H. Khan, A. Rafiq, N. Hussain, A three-step iterative scheme for solving nonlinear \(\phi\)-strongly accretive operator equations in Banach spaces, Fixed Point Theory Appl., 2012 (2012), 1-10
##[12]
S. H. Khan, I. Yildirim, M. Ozdemir , Convergence of a generalized iteration process for two finite families of Lipschitzian pseudocontractive mappings, Math. Comput. Model., 53 (2011), 707-715
##[13]
J. K. Kim, Z. Liu, S. M. Kang, Almost stability of Ishikawa iterative schemes with errors for \(\phi\)-strongly quasi-accretive and \(\phi\)-hemicontractive operators, Commun. Korean Math. Soc., 19 (2004), 267-281
##[14]
Z. Liu, Z. An, Y. Li, S. M. Kang, Iterative approximation of fixed points for \(\phi\)-hemicontractive operators in Banach spaces, Commun. Korean Math. Soc., 19 (2004), 63-74
##[15]
Z. Liu, M. Bounias, S. M. Kang, Iterative approximation of solution to nonlinear equations of \(\phi\)-strongly accretive operators in Banach spaces, Rocky Mountain J. Math., 32 (2002), 981-997
##[16]
Z. Liu, S. M. Kang , Convergence and stability of the Ishikawa iteration procedures with errors for nonlinear equations of the \(\phi\)-strongly accretive type, Neural Parallel Sci. Comput., 9 (2001), 103-118
##[17]
Y. Miao , S. H. Khan, Strong Convergence of an implicit iterative algorithm in Hilbert spaces, Commun. Math. Anal., 4 (2008), 54-60
##[18]
M. O. Osilike, Iterative solution of nonlinear equations of the \(\phi\)-strongly accretive type, J. Math. Anal. Appl, 200 (1996), 259-271
##[19]
M. O. Osilike, Iterative solution of nonlinear \(\phi\)-strongly accretive operator equations in arbitrary Banach spaces, Nonlinear Anal., 36 (1999), 1-9
##[20]
A. Rafiq , Iterative solution of nonlinear equations involving generalized \(\phi\)-hemicontractive mappings, Indian J. Math., 50 (2008), 365-380
##[21]
A. Rafiq, On iterations for families of asymptotically pseudocontractive mappings, Appl. Math. Lett., 24 (2011), 33-38
##[22]
K. K. Tan, H. K. Xu, Iterative solutions to nonlinear equations of strongly accretive operators in Banach spaces, J. Math. Anal. Appl., 178 (1993), 9-21
##[23]
K. K. Tan, H. K. Xu , Approximating fixed points of nonexpansive mappings by the Ishikawa iteration process, J. Math. Anal. Appl., 178 (1993), 301-308
]
Fixed point theorems for multivalued G-contractions in Hausdorff b-Gauge spaces
Fixed point theorems for multivalued G-contractions in Hausdorff b-Gauge spaces
en
en
In this paper, we extend gauge spaces in the setting of b metric spaces and prove fixed point theorems for
multivalued mappings in this new setting endowed with a graph. An example is constructed to substantiate
our result. We also discuss possible application of our result for solving integral equations.
847
855
Muhammad Usman
Ali
Department of Mathematics, School of Natural Sciences
National University of Sciences and Technology H-12
Pakistan
muh_usman_ali@yahoo.com
Tayyab
Kamran
Department of Mathematics
Department of Mathematics, School of Natural Sciences
Quaid-i-Azam University
National University of Sciences and Technology H-12
Pakistan
Pakistan
tayyabkamran@gmail.com
Mihai
Postolache
Department of Mathematics and Informatics
University Politehnica of Bucharest
Romania
mihai@mathem.pub.ro
Gauge space
graph
fixed point
nonlinear integral equation.
Article.34.pdf
[
[1]
R. P. Agarwal, Y. J. Cho, D. O'Regan, Homotopy invariant results on complete gauge spaces, Bull. Austral. Math. Soc., 67 (2003), 241-248
##[2]
S. M. A. Aleomraninejad, Sh. Rezapour, N. Shahzad, Some fixed point results on a metric space with a graph, Topology Appl., 159 (2012), 659-663
##[3]
J. H. Asl, B. Mohammadi, S. Rezapour, S. M. Vaezpour, Some fixed point results for generalized quasi-contractive multifunctions on graphs, Filomat, 27 (2013), 311-315
##[4]
F. Bojor , Fixed point of \(\varphi\)-contraction in metric spaces endowed with a graph, Ann. Univ. Craiova Math. Ser. Mat. Inform., 37 (2010), 85-92
##[5]
F. Bojor, Fixed point theorems for Reich type contractions on metric spaces with a graph, Nonlinear Anal., 75 (2012), 3895-3901
##[6]
F. Bojor, Fixed points of Kannan mappings in metric spaces endowed with a graph, An. St. Univ. Ovidius Constanta Ser. Mat., 20 (2012), 31-40
##[7]
M. Cherichi, B. Samet, C. Vetro, Fixed point theorems in complete gauge spaces and applications to second order nonlinear initial value problems, J. Funct. Space Appl., 2013 (2013), 1-8
##[8]
M. Cherichi, B. Samet , Fixed point theorems on ordered gauge spaces with applications to nonlinear integral equations, Fixed Point Theory Appl., 2012 (2012), 1-19
##[9]
C. Chifu, G. Petrusel, Fixed point results for generalized contractions on ordered gauge spaces with applications, Fixed Point Theory Appl., 2011 (2011), 1-10
##[10]
A. Chis, R. Precup , Continuation theory for general contractions in gauge spaces, Fixed Point Theory Appl., 3 (2004), 173-185
##[11]
S. Czerwik , Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostraviensis, 1 (1993), 5-11
##[12]
S. Czerwik, Non-linear set-valued contraction mappings in b-metric spaces, Atti. Sem. Math. Fig. Univ. Modena, 46 (1998), 263-276
##[13]
J. Dugundji, Topology, Allyn and Bacon,, Boston (1966)
##[14]
M. Frigon , Fixed point results for generalized contractions in gauge spaces and applications, Proc. Amer. Math. Soc., 128 (2000), 2957-2965
##[15]
J. Jachymski , The contraction principle for mappings on a metric space with a graph , Proc. Amer. Math. Soc., 136 (2008), 1359-1373
##[16]
M. Jleli, E. Karapinar, B. Samet , Fixed point results for \(\alpha-\psi_\lambda\)- contractions on gauge spaces and applications, Abstr. Appl. Anal., 2013 (2013), 1-7
##[17]
T. Kamran, M. Samreen, N. Shahzad, Probabilistic G-contractions, Fixed Point Theory Appl., 2013 (2013), 1-14
##[18]
T. Lazara, G. Petrusel , Fixed points for non-self operators in gauge spaces, J. Nonlinear Sci. Appl., 6 (2013), 29-34
##[19]
A. Nicolae, D. O' Regan , A. Petrusel, Fixed point theorems for single-valued and multivalued generalized contractions in metric spaces endowed with a graph, Georgian Math. J., 18 (2011), 307-327
##[20]
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
##[21]
M. Samreen, T. Kamran, Fixed point theorems for integral G-contractions , Fixed Point Theory Appl., 2013 (2013), 1-11
##[22]
M. Samreen, T. Kamran, N. Shahzad, Some fixed point theorems in b-metric space endowed with graph , Abstr. Appl. Anal., 2013 (2013), 1-9
##[23]
W. Shatanawi, A. Pitea, R. Lazovic, Contraction conditions using comparison functions on b-metric spaces, Fixed Point Theory Appl., 2014 (2014), 1-9
##[24]
J. Tiammee, S. Suantai , Coincidence point theorems for graph-preserving multi-valued mappings, Fixed Point Theory Appl., 2014 (2014), 1-11
]
Almost periodicity of impulsive Hematopoiesis model with infinite delay
Almost periodicity of impulsive Hematopoiesis model with infinite delay
en
en
This paper is concerned with almost periodicity of impulsive Hematopoiesis model with infinite delay. By
employing the decreasing operator fixed point theorem, we obtain suficient conditions for the existence
of unique almost periodic positive solution. In addition, the exponential stability is derived by Liapunov
functional.
856
865
Zhijian
Yao
Department of Mathematics and Physics
Anhui Jianzhu University
China
zhijianyao@126.com
Impulsive Hematopoiesis model
infinite delay
almost periodic solution
exponential stability
decreasing operator
fixed point theorem.
Article.35.pdf
[
[1]
D. Bainov, P. Simeonov, Impulsive Differential Equation: Periodic Solutions and Applications, Longman Scientific and Technical, Harlow (1993)
##[2]
D. Bainov, P. Simeonov , System with Impulse Effect: Stability, Theory and Applications, John Wiley and Sons, New York (1989)
##[3]
A. Fink, Almost Periodic Differential Equations, Lecture Notes in Mathematics, Springer, Berlin, (1974), -
##[4]
X. L. Fu, B. Q. Yan, Y. S. Liu, Introduction to Impulsive Differential System (in Chinese), Science Press, Beijing (2005)
##[5]
M. Fan, K. Wang, Global existence of positive periodic solutions of periodic predator-prey system with infinite delays, J. Math. Anal. Appl., 262 (2001), 1-11
##[6]
I. Gyori, G. Ladas, Oscillation Theory of Delay Differential Equations with Applications, Clarendon Press, Oxford (1991)
##[7]
K. Gopalsamy, M. R. S. Kulenovic, G. Ladas, Oscillation and global attractivity in models of Hematopoiesis, J. Dynam. Differential Equations, 2 (1990), 117-132
##[8]
D. Guo, Nonlinear Functional Analysis, Shandong Science and Technology Press, Jinan (2001)
##[9]
C. Y. He , Almost Periodic Differential Equations, Higher Education Press, Beijing (1992)
##[10]
H. F. Huo, W. T. Li, X. Z. Liu, Existence and global attractivity of positive periodic solution of an impulsive delay differential equation, Appl. Anal., 83 (2004), 1279-1290
##[11]
D. Q. Jiang, J. J. Wei , Existence of positive periodic solutions for non-autonomous delay differential equations, Chinese Ann. Math. Ser. A, 20 (1999), 715-720
##[12]
Y. Kuang, Delay Differential Equations with Applications in Population Dynamics, Academic Press, Boston (1993)
##[13]
G. Karakostas, C. G. Philos, Y. G. Sficas, Stable steady state of some population models, J. Dynam. Differential Equations, 4 (1992), 161-190
##[14]
V. Lakshmikantham, D. Bainov, P. Simeonov, Theory of Impulsive Differential Equations, World Scientific Publishing Co., Teaneck (1989)
##[15]
W. T. Li, H. F. Huo , Existence and global attractivity of positive periodic solutions of functional differential equations with impulses, Nonlinear Anal., 59 (2004), 857-877
##[16]
M. C. Mackey, L. Glass, Oscillations and chaos in physiological control systems, Sciences, 197 (1977), 287-289
##[17]
S. H. Saker, Oscillation and global attractivity in Hematopoiesis model with time delay, Appl. Math. Comput., 136 (2003), 241-250
##[18]
S. H. Saker , Oscillation and global attractivity in Hematopoiesis model with periodic coefficients, Appl. Math. Comput., 142 (2003), 477-494
##[19]
A. M. Samoilenko, N. A. Perestyuk, Impulsive Differential Equations, World Scientific, River Edge, NJ (1995)
##[20]
A. Wan, D. Jiang, X. Xu, A new existence theory for positive periodic solutions to functional differential equations, Comput. Math. Appl., 47 (2004), 1257-1262
##[21]
D. Ye, M. Fan, Periodicity in mutualism systems with impulse, Taiwanese J. Math., 10 (2006), 723-737
##[22]
A. Zaghrout, A. Ammar, M. M. A. Elsheikh, Oscillation and global attractivity in delay equation of population dynamics, Appl. Math. Comput., 77 (1996), 195-204
]
Evolutes of null torus fronts
Evolutes of null torus fronts
en
en
The main goal of this paper is to characterize evolutes at singular points of curves in hyperbolic plane by
analysing evolutes of null torus fronts. We have done some work associated with curves with singular points
in Euclidean 2-sphere [H. Yu, D. Pei, X. Cui, J. Nonlinear Sci. Appl., 8 (2015), 678-686]. As a series of
this work, we further discuss the relevance between singular points and geodesic vertices of curves and give
different characterizations of evolutes in the three pseudo-spheres.
866
876
Xiupeng
Cui
School of Mathematics and Statistics
Northeast Normal University
P. R. China
cuixp606@nenu.edu.cn
Donghe
Pei
School of Mathematics and Statistics
Northeast Normal University
P. R. China
peidh340@nenu.edu.cn
Haiou
Yu
School of Mathematics and Statistics
Department of Mathematical Education, College of Humanities and Sciences
Northeast Normal University
Northeast Normal University
P. R. China
P. R. China
yuho930@nenu.edu.cn
Evolute
null torus front
null torus framed curve
hyperbolic plane.
Article.36.pdf
[
[1]
V. I. Arnold, S. M. Gusein-Zade, A. N. Varchenko, Singularities of differentiable maps, Birkhäuser, Boston (1985)
##[2]
V. I. Arnold, Singularities of caustics and wave fronts, Kluwer Academic Publishers, Dordrecht (1990)
##[3]
V. I. Arnold , Topological properties of Legendre projections in contact geometry of wave fronts, St. Petersburg Math. J., 6 (1995), 439-452
##[4]
J. W. Bruce, P. J. Giblin, Curves and singularities, A geometrical introduction to singularity theory, Cambridge University Press, Cambridge (1992)
##[5]
T. Fukunaga, M. Takahashi , Existence and uniqueness for Legendre curves, J. Geom., 104 (2013), 297-307
##[6]
T. Fukunaga, M. Takahashi , Evolutes of fronts in the Euclidean plane, J. Singul., 10 (2014), 92-107
##[7]
G. Ishikawa, S. Janeczko, Symplectic bifurcations of plane curves and isotropic liftings, Q. J. Math., 54 (2003), 73-102
##[8]
S. Izumiya, D. Pei, T. Sano, E. Torii, Evolutes of hyperbolic plane curves, Acta Math. Sin. (Engl. Ser.), 20 (2004), 543-550
##[9]
S. B. Jackson , The four-vertex theorem for surfaces of constant curvature, Amer. J. Math., 67 (1945), 563-582
##[10]
L. Kong, D. Pei , On spacelike curves in hyperbolic space times sphere, Int. J. Geom. Methods Mod. Phys., 2014 (2014), 1-12
##[11]
I. Porteous, The normal singularities of submanifold, J. Differential Geom., 5 (1971), 543-564
##[12]
Z. Wang, D. Pei, L. Chen, Geometry of 1-lightlike submanifolds in anti-de Sitter n-space, Proc. Roy. Soc. Edinburgh Sect. A, 143 (2013), 1089-1113
##[13]
H. Yu, D. Pei, X. Cui, Evolutes of fronts on Euclidean 2-sphere, J. Nonlinear Sci. Appl., 8 (2015), 678-686
]
Oscillation results for nonlinear second-order damped dynamic equations
Oscillation results for nonlinear second-order damped dynamic equations
en
en
The oscillatory behavior of a class of second-order nonlinear dynamic equations with damping on an arbitrary
time scale is considered without requiring explicit sign assumptions on the derivative of the nonlinearity.
Several sufficient conditions for the oscillation of solutions are presented using the Riccati transformation
and integral averaging technique. An illustrative example is provided.
877
883
Jingjing
Wang
School of Information Science & Technology
Qingdao University of Science & Technology
P. R. China
kathy1003@163.com
M. M. A.
El-Sheikh
Department of Mathematics, Faculty of Science
Menoufia University
Egypt
msheikh_1999@yahoo.com
R. A.
Sallam
Department of Mathematics, Faculty of Science
Menoufia University
Egypt
rasallam1@hotmail.com
D. I.
Elimy
Department of Mathematics, Faculty of Science
Menoufia University
Egypt
Dalia−math86@yahoo.com
Tongxing
Li
LinDa Institute of Shandong Provincial Key Laboratory of Network Based Intelligent Computing
Linyi University
P. R. China
litongx2007@163.com
Oscillation
second-order
nonlinear dynamic equation
damping term
time scale.
Article.37.pdf
[
[1]
R. P. Agarwal, M. Bohner, T. Li, Oscillatory behavior of second-order half-linear damped dynamic equations, Appl. Math. Comput., 254 (2015), 408-418
##[2]
R. P. Agarwal, M. Bohner, T. Li, C. Zhang, Oscillation theorems for fourth-order half-linear delay dynamic equations with damping, Mediterr. J. Math., 11 (2014), 463-475
##[3]
R. P. Agarwal, M. Bohner, D. O'Regan, A. Peterson, Dynamic equations on time scales: a survey, J. Comput. Appl. Math., 141 (2002), 1-26
##[4]
M. Bohner, L. Erbe, A. Peterson, Oscillation for nonlinear second order dynamic equations on a time scale, J. Math. Anal. Appl., 301 (2005), 491-507
##[5]
M. Bohner, A. Peterson, Dynamic Equations on Time Scales: An Introduction with Applications, Birkhäuser, Boston (2001)
##[6]
M. Bohner, A. Peterson, Advances in Dynamic Equations on Time Scales, Birkhäuser, Boston (2003)
##[7]
L. Erbe, A. Peterson, An oscillation result for a nonlinear dynamic equation on a time scale, Can. Appl. Math. Q., 11 (2003), 143-157
##[8]
L. Erbe, A. Peterson, Boundedness and oscillation for nonlinear dynamic equations on a time scale, Proc. Amer. Math. Soc., 132 (2004), 735-744
##[9]
L. Erbe, A. Peterson, S. H. Saker, Oscillation criteria for second-order nonlinear dynamic equations on time scales, J. London Math. Soc., 67 (2003), 701-714
##[10]
X. Fu, T. Li, C. Zhang, Oscillation of second-order damped differential equations, Adv. Difference Equ., 2013 (2013), 1-11
##[11]
T. S. Hassan, L. Erbe, A. Peterson, Oscillation of second order superlinear dynamic equations with damping on time scales, Comput. Math. Appl., 59 (2010), 550-558
##[12]
S. Hilger, Analysis on measure chains-a unified approach to continuous and discrete calculus, Results Math., 18 (1990), 18-56
##[13]
M. Kirane, Y. V. Rogovchenko, Oscillation results for a second order damped differential equation with non- monotonous nonlinearity, J. Math. Anal. Appl., 250 (2000), 118-138
##[14]
C. G. Philos, Oscillation theorems for linear differential equations of second order, Arch. Math., 53 (1989), 482-492
##[15]
Y. C. Qiu, Q. R. Wang, Oscillation results for second-order nonlinear damped dynamic equations on time scales, Abstr. Appl. Anal., 2014 (2014), 1-7
##[16]
Y. C. Qiu, Q. R. Wang, Oscillation criteria of second-order dynamic equations with damping on time scales , Abstr. Appl. Anal., 2014 (2014), 1-11
##[17]
Y. V. Rogovchenko, F. Tuncay , Oscillation theorems for a class of second order nonlinear differential equations with damping, Taiwanese J. Math., 13 (2009), 1909-1928
##[18]
S. H. Saker, R. P. Agarwal, D. O'Regan, Oscillation of second-order damped dynamic equations on time scales, J. Math. Anal. Appl., 330 (2007), 1317-1337
##[19]
M. T. Şenel, Kamenev-type oscillation criteria for the second-order nonlinear dynamic equations with damping on time scales, Abstr. Appl. Anal., 2012 (2012), 1-18
]
Existence of nonoscillatory solutions to second-order nonlinear neutral difference equations
Existence of nonoscillatory solutions to second-order nonlinear neutral difference equations
en
en
We study a class of second-order neutral delay difference equations with positive and negative coefficients
\[\Delta(r_n(\Delta(x_n + px_{n-m}))) + p_nf(x_{n-k}) - q_ng(x_{n-l}) = 0, n = n_0, n_0 + 1,...,\]
where \(p \in R, m; k; l; n_0 \in N, p_n; q_n; r_n \in R^+; f; g \in C(R;R)\) with \(xf(x) > 0\) and \(xg(x) > 0 (x \neq 0)\). Some
sufficient conditions for the existence of a nonoscillatory solution of the studied equation expressed in terms
of
\(\sum^\infty R_np_n < 1\) and
\(\sum^\infty R_nq_n < 1\) are obtained, where\(R_n = \sum^n _{s=n_0} \frac{1 }{r_s} ; n \geq n_0\).
884
892
Yazhou
Tian
School of Electronic and Information Engineering
Xi'an Jiaotong University
Qingdao Technological University
P. R. China
P. R. China
tianyazhou369@163.com
Yuanli
Cai
School of Electronic and Information Engineering
Xi'an Jiaotong University
P. R. China
ylicai@mail.xjtu.edu.cn
Tongxing
Li
Qingdao Technological University
P. R. China
litongx2007@163.com
Nonoscillatory solution
neutral delay difference equation
second-order
positive and negative coefficients.
Article.38.pdf
[
[1]
R. P. Agarwal, M. Bohner, S. R. Grace, D. O'Regan, Discrete Oscillation Theory, Hindawi Publishing Corporation, New York (2005)
##[2]
R. P. Agarwal, P. J. Y. Wong, Advanced Topics in Difference Equations, Kluwer Academic Publishers, Dordeecht (1997)
##[3]
T. Candan, The existence of nonoscillatory solutions of higher order nonlinear neutral equations, Appl. Math. Lett., 25 (2012), 412-416
##[4]
T. Candan, R. S. Dahiya, Existence of nonoscillatory solutions of first and second order neutral differential equations with distributed deviating arguments, J. Franklin Inst., 347 (2010), 1309-1316
##[5]
S. Chen, C. Li, Nonoscillatory solutions of second order nonlinear difference equations, Appl. Math. Comput., 205 (2008), 478-481
##[6]
J. Cheng, Existence of a nonoscillatory solution of a second-order linear neutral difference equation, Appl. Math. Lett., 20 (2007), 892-899
##[7]
B. S. Lalli, B. G. Zhang, On existence of positive solutions and bounded oscillations for neutral difference equations, J. Math. Anal. Appl., 166 (1992), 272-287
##[8]
T. Li, Z. Han, S. Sun, D. Yang, Existence of nonoscillatory solutions to second-order neutral delay dynamic equations on time scales, Adv. Difference Equ., 2009 (2009), 1-10
##[9]
W. T. Li, X. L. Fan, C. k. Zhong, On unbounded positive solutions of second-order difference equations with a singular nonlinear term, J. Math. Anal. Appl., 246 (2000), 80-88
##[10]
H. Peics, Positive solutions of second-order linear difference equation with variable delays, Adv. Difference Equ., 2013 (2013), 1-12
##[11]
Y. Tian, F. Meng, Existence for nonoscillatory solutions of higher-order nonlinear differential equations, ISRN Math. Anal., 2011 (2011), 1-9
##[12]
J. Yan, Existence of oscillatory solutions of forced second order delay differential equations, Appl. Math. Lett., 24 (2011), 1455-1460
##[13]
B. G. Zhang, Y. Zhou, Oscillation and nonoscillation for second-order linear difference equations, Comput. Math. Appl., 39 (2000), 1-7
]
Boundedness and asymptotic behavior of positive solutions for difference equations of exponential form
Boundedness and asymptotic behavior of positive solutions for difference equations of exponential form
en
en
In this paper we study the boundedness and the asymptotic behavior of the positive solutions of the difference
equation
\[x_{n+1} = a + bx_ne^{-x_{n-1}},\]
where \(a; b\) are positive constants, and the initial values \(x_{-1}; x_0\) are positive numbers.
893
899
Huili
Ma
Department of Mathematics
Northwest Normal University
China
mahuili@nwnu.edu.cn
Hui
Feng
Department of Mathematics
Northwest Normal University
China
fh_9237@163.com
Jiaofeng
Wang
Department of Mathematics
Northwest Normal University
China
1529189732@qq.com
Wandi
Ding
Department of Mathematics
Middle Tennessee State University
USA
Wandi.Ding@mtsu.edu
Difference equations
boundedness
asymptotic stability.
Article.39.pdf
[
[1]
R. Devault, W. Kosmala, G. Ladas, S. W. Schultz, Global Behavior of \(y_{n+1} =\frac{ p+y_{n-k}}{ qy_n+y_{n-k}}\), Nonlinear Anal., 47 (2001), 4743-4751
##[2]
H. El-Metwally, E. A. Grove, G. Ladas, R. Levins, M. Radin, On the difference equation \(x_{n+1} = \alpha+\beta x_{n-1}e^{x_n}\), Nonlinear Anal., 47 (2001), 4623-4634
##[3]
N. Fotiades, G. Papaschinopoulos, Existence, uniqueness and attractivity of prime period two solution for a difference equation of exponential form, Math. Comput. Model., 218 (2012), 11648-11653
##[4]
M. R. S. Kulenovic, G. Ladas, W. S. Sizer, On the Recursive Sequence \(x_{n+1} =\frac{ \alpha x_n+\beta x_{n-1}}{\gamma x_n+\delta x_{n-1}}\), Math. Sci. Res. Hot-Line, 2 (1998), 1-16
##[5]
G. Papaschinopoulos, M. Radin, C. J. Schinas, On the system of two difference equations of exponetial form: \(x_{n+1 }= a + bx_{n-1}e^{-y_n}; y_{n+1} = c + dy_{n-1}e^{-x_n}\), Math. Comput. Model., 54 (2011), 2969-2977
##[6]
G. Stefanidou, G. Papaschinopoulos, C. J. Schinas, On a system of two exponential type difference equations, Comm. Appl. Nonlinear Anal., 17 (2010), 1-13
]