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Minimax Theory and its Applications 01 (2016), No. 1, 111--124
Copyright Heldermann Verlag 2016

A Concave-Convex Ky Fan Minimax Inequality

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

In the form most frequently used in scalar generalizations of the celebrated Ky Fan minimax inequality, some topological hypotheses and one convexity condition are assumed. In this work we introduce a Ky Fan minimax inequality where the convexity assumption is replaced by a concavity-convexity requirement: a slightly restrictive concavity property on one variable and a new convexity condition, necessary for the validity of such an inequality, in the another one. Our result is different from the aforementioned extensions of the Ky Fan minimax inequality and moreover avoids their vectorial setting.

Keywords: Ky Fan's minimax inequality, minimax inequalities, inf-diagonal convexity.

MSC: 49J35, 49K35, 26B25

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