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Journal of Convex Analysis 21 (2014), No. 4, 1105--1139
Copyright Heldermann Verlag 2014

An Intrinsic Notion of Convexity for Minimax

M. Ruiz Galán
Dept. of Applied Mathematics, E.T.S. Ingeniería de Edificación, University of Granada, c/ Severo Ochoa s/n, 18071 Granada, Spain

A proper extension of Fan's minimax theorem, sharp in a sense, is provided. In particular, a natural kind of convexity for minimax inequalities arises. In addition a vector-valued Lax-Milgram theorem is derived, which in turn implies a characterization of the solvability of systems with infinitely many variational equations.

Keywords: Minimax theorems, Lax-Milgram theorem, variational equations.

MSC: 49K35, 49J40, 58E30

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