Borsuk’s antipodal fixed points theorems for compact or condensing set-valued maps

Abstract

We give a generalized version of the well-known Borsuk’s antipodal fixed point theorem for a large class of antipodally approachable condensing or compact set-valued maps defined on closed subsets of locally convex topological vector spaces. These results contain corresponding results obtained in the literature for compact set-valued maps with convex values.

Keywords

• borsuk’s antipodal fixed point theorem
• approximative selection
• antipodally approximable set-valued maps
• compact set-valued maps
• measure of non-compactness
• condensing set-valued maps
• 47h10
• 54c60