The KKM Theorem in Modular Spaces and Applications to Minimax Inequalities

Abstract

In this paper, we present a modular version of KKM and generalized KKM mappings and then we establish a characterization of generalized KKM mappings in modular spaces. Also we prove an analogue to KKM principle in modular spaces. Moreover, as an application, we give some sufficient conditions which guarantee existence of solutions of minimax problems in which we get Fan’s minimax inequality in modular spaces.