Strong convergence of approximated sequences for nonexpansive mappings in Banach spaces

Abstract

In this paper, we study the convergence of the sequence defined by \[ x_0\in C , \;\; x_{n+1} = \alpha _{n}x + (1-\alpha _{n})Tx_n , \;\; n=0,1,2, \ldots ,\] where $0 \leq \alpha _n \leq 1$ and $T$ is a nonexpansive mapping from a closed convex subset of a Banach space into itself.