WEAK CONVERGENCE THEOREM FOR NEW NONEXPANSIVE MAPPINGS IN BANACH SPACES AND ITS APPLICATIONS

Abstract

A new nonexpansive mapping in a Banach space which is called generalized nonexpansive was introduced by the authors [4]. In this paper, we prove a weak convergence theorem for finding a fixed point of a generalized nonexpansive mapping in a Banach space. Moreover, using this result, we consider a proximal-type algorithm and the feasibility problem.