Strong convergence of modified iterative algorithm for family of asymptotically nonexpansive mappings

Document Type : Research Paper


Michael Okpara University of Agriculture, Umudike, Abia State, Nigeria


In this paper we introduce new modified implicit and explicit algorithms and prove strong convergence of the two algorithms to a common fixed point of a family of uniformly asymptotically regular asymptotically nonexpansive mappings in a real reflexive Banach space  with a uniformly G$\hat{a}$teaux differentiable norm. Our result is applicable in $L_{p}(\ell_{p})$ spaces, $1 < p <\infty$ and consequently in sobolev spaces.