Fixed point theorems for a sum of two mappings in locally convex spaces

P Vijayaraju

doi:10.1155/s0161171294000967

Abstract

Cain and Nashed generalized to locally convex spaces a well known fixed point theorem of Krasnoselskii for a sum of contraction and compact mappings in Banach spaces. The class of asymptotically nonexpansive mappings includes properly the class of nonexpansive mappings as well as the class of contraction mappings. In this paper, we prove by using the same method some results concerning the existence of fixed points for a sum of nonexpansive and continuous mappings and also a sum of asymptotically nonexpansive and continuous mappings in locally convex spaces. These results extend a result of Cain and Nashed.

Highlights

Let K be a nonempty closed convex bounded subset of a Banach space x
Sehgal and Singh [9] generalized the above result of Cain and Nashed [2] to a sum T + S of a nonlinear contraction mapping T of K into X and a continuous mapping S of K into X
The aim of this paper is to prove fixed point theorems for a sum of nonexpansive and continuous mappings in locally convex spaces

Summary

Introduction

Let K be a nonempty closed convex bounded subset of a Banach space x. Nashed and Wong [7] generalized Krasnoselskii’s theorem to sum T + S of a nonlinear contraction mapping T of K into X (that is, [[Tz-Ty[[

Objectives

Results

Conclusion