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

Ugwunnadi, Godwin Chidi

doi:10.22075/ijnaa.2016.479

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

Document Type : Research Paper

Author

Godwin Chidi Ugwunnadi

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

10.22075/ijnaa.2016.479

Abstract

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.

Keywords

Fixed point

Banach space

Asymptotically nonexpansive mapping