Existence of solutions for generalized symmetric vector quasi-equilibrium problems in abstract convex spaces with applications
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Authors
Wei-Bing Zhang
- Department of Information and computing science, Chengdu Technological University, Chengdu, 611730, P. R. China.
Wen-Yong Yan
- Department of Information and computing science, Chengdu Technological University, Chengdu, 611730, P. R. China.
Abstract
In this paper, we introduce and study a class of generalized symmetric vector quasi-equilibrium problems
in abstract convex spaces. By virtue of the properties of \(\Gamma\)-convex and KC-map, we give some sufficient
conditions to guarantee the existence of solutions for the generalized symmetric vector quasi-equilibrium
problems in abstract convex spaces. As application, we show an existence theorem of solutions for the
generalized semi-infinite programs with generalized symmetric vector quasi-equilibrium constraints.
Share and Cite
ISRP Style
Wei-Bing Zhang, Wen-Yong Yan, Existence of solutions for generalized symmetric vector quasi-equilibrium problems in abstract convex spaces with applications, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 6, 4399--4408
AMA Style
Zhang Wei-Bing, Yan Wen-Yong, Existence of solutions for generalized symmetric vector quasi-equilibrium problems in abstract convex spaces with applications. J. Nonlinear Sci. Appl. (2016); 9(6):4399--4408
Chicago/Turabian Style
Zhang, Wei-Bing, Yan, Wen-Yong. "Existence of solutions for generalized symmetric vector quasi-equilibrium problems in abstract convex spaces with applications." Journal of Nonlinear Sciences and Applications, 9, no. 6 (2016): 4399--4408
Keywords
- Abstract convex space
- generalized symmetric vector quasi-equilibrium problem
- semi-infinite program
- \(\Gamma\)-convex
- KKM mapping.
MSC
References
-
[1]
A. Amini-Harandi, Best and coupled best approximation theorems in abstract convex metric spaces, Nonlinear Anal., 74 (2011), 922-926.
-
[2]
L. Q. Anh, P. Q. Khanh , Various kinds of semicontinuity and the solution sets of parametric multivalued symmetric vector quasiequilibrium problems, J. Glob. Optim., 41 (2008), 539-558.
-
[3]
J. P. Aubin, A. Cellina, Differential Inclusions, Springer-Verlag, Berlin (1984)
-
[4]
A. Basu, K. Martin, C. T. Ryan , On the sufficiency of finite support duals in semi-infinite linear programming, Oper. Res. Lett., 42 (2014), 16-20.
-
[5]
C. Berge, Topological Spaces, Oliver and Boyd, London (1963)
-
[6]
J. C. Chen, X. H. Gong, The stability of set of solutions for symmetric vector quasi-equilibrium problems, J. Optim. Theory Appl., 136 (2008), 359-374.
-
[7]
G. Y. Chen, X. Huang, X. Yang, Vector optimization: set-valued and variational analysis, Springer Science & Business Media, Berlin (2006)
-
[8]
Y. J. Cho, M. Rostamian Delavar, S. A. Mohammadzadeh, M. Roohi , Coincidence theorems and minimax inequalities in abstract convex spaces, J. Inqual. Appl., 2011 (2011), 14 pages.
-
[9]
U. Faigle, W. Kern, G. Still , Algorithmic principles of mathematical programming, Kluwer Academic Publishers, Dordrecht (2003)
-
[10]
M. Fakhar, J. Zafarani , Generalized symmetric vector quasiequilibrium problems, J. Optim. Theory Appl., 136 (2008), 397-409.
-
[11]
F. Ferro , Optimization and stability results through cone lower semicontinuity, Set-Valued Anal., 5 (1997), 365-375.
-
[12]
J. Y. Fu, Symmetric vector quasi-equilibrium problems, J. Math. Anal. Appl., 285 (2003), 708-713.
-
[13]
M. Fukushima, J. S. Pang, Some feasibility issues in mathematical programs with equilibrium constraints, SIAM J. Optim., 8 (1998), 673-681.
-
[14]
X. H. Gong , Symmetric strong vector quasi-equilibrium problems , Math. Methods Oper. Res., 65 (2007), 305-314.
-
[15]
F. Guerra Vázquez, J. J. Rückmann, O. Steinc, G. Stilld , Generalized semi-infinite programming: A tutorial, J. Comput. Appl. Math., 217 (2008), 394-419.
-
[16]
O. Güler, Foundations of Optimization, Springer, New York (2010)
-
[17]
Y. Han, X. H. Gong, Levitin-Polyak well-posedness of symmetric vector quasi-equilibrium problems, Optimization, 64 (2014), 1537-1545.
-
[18]
J. Jahn, Vector Optimization: Theory, Applications, and Extensions, Springer-Verlag, Berlin (2004)
-
[19]
X. B. Li, X. J. Long, Z. Lin, Stability of solution mapping for parametric symmetric vector equilibrium problems, J. Ind. Manag Optim., 11 (2015), 661-671.
-
[20]
L. J. Lin , Existence results for primal and dual generalized vector equilibrium problems with applications to generalized semi-infinite programming, J. Global Optim., 33 (2005), 579-595.
-
[21]
X. W. Liu, Y. Zhang, R. X. Tan , Fixed point theorems for better admissible multimaps on abstract convex spaces, Appl. Math. J. Chinese Univ. Ser. B, 25 (2010), 55-62.
-
[22]
X. J. Long, N. J. Huang , Metric characterizations of \(\alpha\)-well-posedness for symmetric quasi-equilibrium problems , J. Global Optim., 45 (2009), 459-471.
-
[23]
H. Lu, Q. Hu , A collectively fixed point theorem in abstract convex spaces and its applications, J. Funct. Spaces Appl., 2013 (2013), 10 pages.
-
[24]
D. T. Luc , Theory of vector optimization, Springer, Berlin (1989)
-
[25]
Z. Q. Luo, J. S. Pang, D. Ralph, Mathematical programs with equilibrium constraints, Cambrige University Press, Cambridge (1996)
-
[26]
S. Park, On generalizations of the KKM principle on abstract convex spaces, Nonlinear Anal. Forum, 11 (2006), 67-77.
-
[27]
S. Park, Generalized convex spaces, L-spaces, and FC-spaces, J. Global Optim., 45 (2009), 203-210.
-
[28]
S. Park , The KKM Principle in abstract convex spaces: equivalent formulations and applications, Nonlinear Anal., 73 (2010), 1028-1042.
-
[29]
S. Park , Remarks on fixed points, maximal elements, and equilibria of economies in abstract convex spaces: revisited, Nonlinear Anal. Forum, 19 (2014), 109-118.
-
[30]
N. X. Tan, Quasi-variational inequilities in topological linear locally convex Hausdorff spaces, Math. Nachr., 122 (1985), 231-245.
-
[31]
G. W. Weber, A. Tezel , On generalized semi-infinite optimization of genetic networks, TOP, 15 (2007), 65-77.
-
[32]
M. G. Yang, N. J. Huang , Coincidence theorems for noncompact KC-maps in abstract convex spaces with applications, Bull. Korean Math. Soc., 6 (2012), 1147-1161.
-
[33]
M. G. Yang, N. J. Huang, Existence results for generalized vector equilibrium problems with applications, Appl. Math. Mech., 35 (2014), 913-924.
-
[34]
M. G. Yang, N. J. Huang, C. S. Lee, Coincidence and maximal element theorems in abstract convex spaces with applications, Taiwanese J. Math., 15 (2011), 13-29.
-
[35]
W. B. Zhang, S. Q. Shan, N. J. Huang, Existence of solutions for generalized vector quasi-equilibrium problems in abstract convex spaces with applications, Fixed Point Theory Appl., 2015 (2015), 23 pages.