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

In this paper we introduce new modied implicit and explicit algorithms and prove strong convergence of the two algorithms to a common xed point of a family of uniformly asymptotically regular asymptotically nonexpansive mappings in a real re exive Banach space with a uniformly G^ateaux differentiable norm. Our result is applicable in Lp(lp) spaces, 1 < p < 1 and consequently in sobolev spaces.