Strong convergence of modified Mann iteration method for an infinite family of nonexpansive mappings in a Banach space

Issara Inchan

Abstract

In this paper we introduce a new modified Mann iteration for a W -mapping generated by $T_n, T_{n-1},\ldots,T_1$ and $\lambda_n, \lambda{n-1},\ldots,\lambda_1$. The iteration is defined as follows: where $W_n$ is a W -mapping, C a nonempty closed convex subset of a Banach space E with uniformly Gba teaux differentiable. Then we prove that under certain different control conditions on the sequences $\{\alpha_n\}$ and $\{\beta_n\}$, that $\{x_n\}$ converges strongly to a common fixed point of $T_n, n \in \mathbb{N}$.