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Zbl 1023.49014
Lin, L.J.; Yu, Z.T.; Kassay, G.
Existence of equilibria for multivalued mappings and its application to vectorial equilibria. (English)
[J] J. Optimization Theory Appl. 114, No.1, 189-208 (2002). ISSN 0022-3239; ISSN 1573-2878/e

Summary: We apply a new fixed-point theorem [{\it L.-J. Lin} and {\it Z.-T. Yu}, Nonlinear Anal., Theory Methods Appl. 43A, 987-999 (2001; Zbl 0989.47051)] and use various monotonicity and some coercivity conditions to establish equilibrium theorems for multimaps in generalized convex spaces of {\it S. Park} and {\it H. Kim} [J. Math. Anal. Appl. 197, 173-187 (1996; Zbl 0851.54039)]. As a simple consequence, we give a unified approach to vectorial equilibria for multimaps. We show that, from our results, some well-known classical results, such as the Ky Fan minimax inequality theorem and the Browder and Hartman-Stampacchia theorems concerning the existence for variational inequalities, can be derived easily.

MSC 2000:: *49J53 Set-valued and variational analysis
90C47 Minimax problems
47N10 Appl. of operator theory in optimization, math. programming, etc.
47H04 Set-valued operators
90C29 Multi-objective programming, etc.

Keywords: transfer open multimap; vectorial equilibria; Cx-quasiconvex-like mapping; G-convex space; upper semicontinuity; minimax inequalities

Citations: Zbl 0989.47051; Zbl 0851.54039

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