Fixed point theorems for sum of two mappings on not necessarily convex subset of a locally convex space

Abstract

In this paper, we prove some fixed point theorems for sum of two mappings in locally convex space. The results generalized the fixed point theorem of Cain and Nashed [2] for sum of two mappings on a convex subset of a locally convex space to sum of two mappings defined on almost convex subset as well as star-shaped subset of a locally convex space.