Approximation of fixed points for a representation of nonexpansive mappings in Banach spaces

Abstract

The purpose of this paper is to study an implicit scheme for a representation of nonexpansive mappings on a closed convex subset of a smooth and uniformly convex Banach space with respect to a left regular sequence of means defined on an appropriate space of bounded real valued functions of the semigroup. This algorithm extends the algorithm that introduced in [N. Hussain, M. L. Bami and E. Soori, An implicit method for finding a common fixed point of a representation of nonexpansive mappings in Banach spaces, Fixed Point Theory and Applications 2014, 2014:238].