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Zbl 1020.46026
Park, Sehie
Some equilibrium problems in generalized convex spaces. (English)
[J] Acta Math. Vietnam. 26, No.3, 349-364 (2001). ISSN 0251-4184

Summary: We show how the fundamental theorems on equilibrium problems can be extended to generalized convex spaces. More precisely, most of important results in the KKM theory hold without assuming the linearity in topological vector spaces. Such examples are the KKM theorem, the minimax theorem and the intersection lemma of von Neumann, the Nash equilibrium theorem, various fixed point theorems, Ky Fan's minimax inequality, variational inequalities, best approximation theorems, existence theorems for solutions of generalized quasi-equilibrium problems, and others.

MSC 2000:: *46N10 Appl. of functional analysis in optimization and math. programming
46A55 Convexity in topological linear spaces
49J35 Minimax problems (existence)
49J40 Variational methods including variational inequalities
90C30 Nonlinear programming

Keywords: KKM theorem; Nash equilibrium theorem; Ky Fan's minimax inequality

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