Maximal Elements and Coincident Points for Couple-Majorized Mappings in Product Topological Vector Spaces

Abstract

By introducing a concept called ’couple-majorized mapping’ in product topoogical vector spaces we establish existence theorems of maximal elements for couple.majorized set-valued families with arbitrary index set. As applications, some component coincidence and fixed points theorems are given which could be regarded as product extension version of the Fan-Browder fixed point theorem and related coincidence theorems. Finally, a coincidence theorem is used to derive the Sion minimax inequality in the case of two functions.