Strong convergence of modified iterative algorithm for family of asymptotically nonexpansive mappings
Godwin Chidi Ugwunnadi · International journal of nonlinear analysis and applications · 2016
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.