- Research Article
- Open access
- Published:
Generalized vector quasi-equilibrium problems with set-valued mappings
Journal of Inequalities and Applications volume 2006, Article number: 69252 (2006)
Abstract
A new mathematical model of generalized vector quasiequilibrium problem with set-valued mappings is introduced, and several existence results of a solution for the generalized vector quasiequilibrium problem with and without-condensing mapping are shown. The results in this paper extend and unify those results in the literature.
References
Ansari QH, Flores-Bazán F: Generalized vector quasi-equilibrium problems with applications. Journal of Mathematical Analysis and Applications 2003,277(1):246–256. 10.1016/S0022-247X(02)00535-8
Ansari QH, Yao J-C: An existence result for the generalized vector equilibrium problem. Applied Mathematics Letters 1999,12(8):53–56. 10.1016/S0893-9659(99)00121-4
Aubin J-P, Ekeland I: Applied Nonlinear Analysis, Pure and Applied Mathematics (New York). John Wiley & Sons, New York; 1984:xi+518.
Chan D, Pang JS: The generalized quasivariational inequality problem. Mathematics of Operations Research 1982,7(2):211–222. 10.1287/moor.7.2.211
Chang S-S, Lee BS, Wu X, Cho YJ, Lee GM: On the generalized quasi-variational inequality problems. Journal of Mathematical Analysis and Applications 1996,203(3):686–711. 10.1006/jmaa.1996.0406
Chen M-P, Lin L-J, Park S: Remarks on generalized quasi-equilibrium problems. Nonlinear Analysis 2003,52(2):433–444. 10.1016/S0362-546X(02)00106-2
Chiang Y, Chadli O, Yao JC: Existence of solutions to implicit vector variational inequalities. Journal of Optimization Theory and Applications 2003,116(2):251–264. 10.1023/A:1022472103162
Cubiotti P: A note on Chan and Pang's existence theorem for generalized quasi-variational inequalities. Applied Mathematics Letters 1996,9(3):73–76. 10.1016/0893-9659(96)00035-3
Fitzpatrick PM, Petryshyn WV: Fixed point theorems for multivalued noncompact acyclic mappings. Pacific Journal of Mathematics 1974,54(2):17–23.
Fu J-Y, Wan A-H: Generalized vector equilibrium problems with set-valued mappings. Mathematical Methods of Operations Research 2002,56(2):259–268. 10.1007/s001860200208
Kim WK: Existence of maximal element and equilibrium for a nonparacompact-person game. Proceedings of the American Mathematical Society 1992,116(3):797–807.
Lin L-J, Park S: On some generalized quasi-equilibrium problems. Journal of Mathematical Analysis and Applications 1998,224(2):167–181. 10.1006/jmaa.1998.5964
Lin L-J, Yu Z-T: Fixed points theorems of KKM-type maps. Nonlinear Analysis 1999,38(2):265–275. 10.1016/S0362-546X(98)00194-1
Mehta G, Tan K-K, Yuan X-Z: Fixed points, maximal elements and equilibria of generalized games. Nonlinear Analysis 1997,28(4):689–699. 10.1016/0362-546X(95)00183-V
Peng J-W: Generalized set-valued equilibrium problems in topological vector spaces. Journal of Chongqing Normal University 2000,17(4):36–40.
Peng J-W: Generalized vectorial quasi-equilibrium problem on-space. Journal of Mathematical Research and Exposition 2002,22(4):519–524.
Su CH, Sehgal VM: Some fixed point theorems for condensing multifunctions in locally convex spaces. Proceedings of the American Mathematical Society 1975,50(1):150–154. 10.1090/S0002-9939-1975-0380530-7
Tian GQ, Zhou JX: Quasi-variational inequalities without the concavity assumption. Journal of Mathematical Analysis and Applications 1993,172(1):289–299. 10.1006/jmaa.1993.1025
Wu X, Shen SK: A further generalization of Yannelis-Prabhakar's continuous selection theorem and its applications. Journal of Mathematical Analysis and Applications 1996,197(1):61–74. 10.1006/jmaa.1996.0007
Yuan GX-Z: Remarks on quasi-variational inequalities and fixed points in locally convex topological vector spaces. Applied Mathematics Letters 1997,10(6):55–61. 10.1016/S0893-9659(97)00105-5
Yuan X-Z, Tarafdar E: Generalized quasi-variational inequalities and some applications. Nonlinear Analysis, Theory, Methods & Applications 1997,29(1):27–40. 10.1016/S0362-546X(96)00019-3
Zhang SS: Variational Inequalities and Complementarity Problem Theory with Applications. Shanghai Science and Technology, Shanghai; 1991.
Zhou JX, Chen G: Diagonal convexity conditions for problems in convex analysis and quasi-variational inequalities. Journal of Mathematical Analysis and Applications 1988,132(1):213–225. 10.1016/0022-247X(88)90054-6
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License ( https://creativecommons.org/licenses/by/2.0 ), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
About this article
Cite this article
Peng, J.W., Zhu, D.L. Generalized vector quasi-equilibrium problems with set-valued mappings. J Inequal Appl 2006, 69252 (2006). https://doi.org/10.1155/JIA/2006/69252
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1155/JIA/2006/69252