KY FAN'S INEQUALITY IN THE CONTEXT OF RELATIVE CONVEXITY

摘要

In this paper we extend the classical Ky Fan inequality into the framework of relative convexity. More precisely, we prove that Ky Fan type minimax inequality holds even outside to the classical convexity settings, namely relative convexity assumptions. The strategy used appeals to a Knaster-Kuratowsky-Mazurkievich argument. As applications, we solve a generalized equilibrium problem and a Nash equilibrium existence theorem is obtained.