Abstract
In this paper, we establish the existence theorems of the generalized vector quasi-equilibrium problems. From some existence theorem, we establish fixed point theorems for a family of lower semicontinuous or nonexpansive multivalued mappings. We also obtain the existence theorems of system of mixed generalized vector variational-like inequalities and existence theorems of the Debreu vector equilibrium problems and the Nash vector equilibrium problems.
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Q.H. Ansari S. Schaible J.C. Yao (2000) ArticleTitleThe system of vector equilibrium problems and its applications Journal of Optim Theory and Applications. 107 547–557
Q.H. Ansari S. Schaible J.C. Yao (2000) ArticleTitleThe system of generalized vector equilibrium problems with applications Journal of Global Optim. 22 3–16
Q.H. Ansari W.K. Chan X.Q. Yang (2004) ArticleTitleThe system of vector quasi-equilibrium problems with applications Journal of Global Optim. 29 45–57
J.P. Aubin A. Cellina (1994) Differential Inclusions Springer Verlag Berlin, Heidelberg, Germany
E. Blum W. Oettli (1994) ArticleTitleFrom optimization and variational inequalities to equilibrium problem The Mathematical Students. 63 123–146
F.E. Browder (1965) ArticleTitleNonexpansive nonlinear operators in a Banach space Proceeding National Academic Science USA. 54 1041–1044
F.E. Browder (1968) ArticleTitleThe fixed point theorem of multivalued mappings in topological linear spaces Mathamatical Annal. 177 283–301
M.P Chen L.J. Lin S. Park (2003) ArticleTitleRemarks on generalized quasi-equilibrium problems Nonlinear Analysis. 52 433–444 Occurrence Handle10.1016/S0362-546X(02)00106-2
G. Debreu (1952) ArticleTitleA social equilibrium existence theorem Proceeding National Academic Science USA. 38 886–893
P. Deguire K.K. Tan G.X.Z. Yuan (1999) ArticleTitleThe study of maximal elements fixed point for Ls-majorized mappings and the quasi-variational inequalities in product spaces Nonlinear Analysis. 37 933–951 Occurrence Handle10.1016/S0362-546X(98)00084-4
X.P. Ding E. Tarafdar (2000) Generalized vector variational-like inequalities without monotonicity F Giannessi (Eds) Vector Variational Inequalities and Vector Equilibria: Mathematical Theorem. Kluwer Academic Publishers Dordrecht, Holland 113–124
J.Y. Fu A.H. Wan (2002) ArticleTitleGeneralized vector equilibria problems with set-valued mappings Mathematical Methods Operativen Research. 56 259–268
D. Gohde (1965) ArticleTitleZum Prinzip der kontraktuen Abbildung Mathematical Nachs. 30 251–258
K. Goebel W.A. Kirk (1990) Topics in Metric Fixed Point Theorem Cambridge University Press Cambridge
N. Hadjisavvas S. Schaible (1998) ArticleTitleFrom scalar to vector equilibrium problem in the quasimonotone case Journal of Optim Theory and Applications. 96 297–307
W.A. Kirk (1965) ArticleTitleA fixed point theorem for mappings which do not increase distance American Mathematical Monthly 72 1004–1006
Kirk, W.A. (1986), Nonexpansive mapping on product spaces, set-valued mappings, k-uniform rotundity, nonlinear functional analysis and its applications. In:Browder, F.E. (ed.), American Mathematical Society Symposium Pure Mathematical 45, 51–64.
Khanh, P.Q. and Luu, L.M. Some existence results for vector quasi-variational inequalities involving multifunctions and applications to traffic equilibrium problems, Journal of Global Optim (to appear).
L.J. Lin S. Park (1998) ArticleTitleOn some generalized quasi-equilibrium problems Journal of Mathematical Analysis Applications. 224 167–181
L.J. Lin Z.T. Yu (2001) ArticleTitleFixed point theorems and equilibrium problems Nonlinear Analysis. 43 987–999 Occurrence Handle10.1016/S0362-546X(99)00202-3
L.J. Lin Z.T. Yu G. Kassay (2002) ArticleTitleExistence of equilibrium for multivalued mappings and its applications to vectorial equilibira Journal of Optim Theory and Applications. 114 189–208
L.J. Lin Q.H. Ansari J.Y. Wu (2003) ArticleTitleGeometric properties and coincidence theorems with applications to generalized vector equilibrium problem Journal of Optim Theory and Applications. 117 121–137
Lin, L.J. and Ansari, Q.H., Some existence results for solutions of generalized vector quasi-equilibrium problems (to appear).
L.J. Lin Z.T. Yu (2001) ArticleTitleOn some equilibrium problems for multivalued maps Journal of Computational Applied Mathematics. 129 171–183
Lin, L.J., Chen, L.F. and Ansari, Q.H., Generalized abstract economy and solution of generalized vector quasi problems, Journal of Optimization Theory and Applications (to appear).
Lin, L.J. and Liu, Y.H. Existence theorems of system of generalized vector quasi- equilibrium problems and optimization problems, (preprint).
J. Nash (1951) ArticleTitleNon-cooperative games Annals of Mathematics. 54 286–295
W. Takahashi (2000) Nonlinear Functional Analysis Yokohama Publishers Yokohama
N.X. Tan (1985) ArticleTitleQuasi-variational inequalities in topological linear locally convex Hausdorff spaces Mathematicsche Nachrichen. 122 231–245
X. Wu (1997) ArticleTitleA new fixed point theorem and its applications Proceeding American Mathematical Society. 125 1179–1183
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Lin, Lj. System of Generalized Vector Quasi-Equilibrium Problems with Applications to Fixed Point Theorems for a Family of Nonexpansive Multivalued Mappings. J Glob Optim 34, 15–32 (2006). https://doi.org/10.1007/s10898-005-4702-y
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DOI: https://doi.org/10.1007/s10898-005-4702-y