, Volume 58, Issue 3, pp 269-278
Date: 16 Jun 2013

An intersection theorem for set-valued mappings

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Abstract

Given a nonempty convex set X in a locally convex Hausdorff topological vector space, a nonempty set Y and two set-valued mappings T: XX, S: YX we prove that under suitable conditions one can find an xX which is simultaneously a fixed point for T and a common point for the family of values of S. Applying our intersection theorem, we establish a common fixed point theorem, a saddle point theorem, as well as existence results for the solutions of some equilibrium and complementarity problems.