Iterative approximation to common fixed points of a countable family of nonexpansive mappings

Abstract

We proved several strong convergence results by using the conception of a uniformly asymptotically regular sequence {T n } of nonexpansive mappings in a reflexive Banach space which admits a weakly continuous duality mapping J ϕ(l p (1 < p < ∞) has a weakly continuous duality map with gauge ϕ(t) = t p−1. The results presented develop and complement the corresponding ones by Song, Y. and Chen, R., 2007 [Iterative approximation to common fixed points of nonexpansive mapping sequences in reflexive Banach spaces. Nonlinear Analysis, 66, 591–603], Song, Y., Chen, R. and Zhou, H., 2007 [Viscosity approximation methods for nonexpansive mapping sequences in Banach spaces. Nonlinear Analysis, 66, 1016–1024] and O'Hara, J.G., Pillay, P. and Xu, H.K., 2006 [Iterative approaches to convex feasibility problem in Banach Space. Nonlinear Analysis, 64, 2022–2042], O'Hara, J.G., Pillay, P. and Xu, H.K., 2003 [Iterative approaches to fineding nearest common fixed point of nonexpansive mappings in Hilbert spaces. Nonlinear Analysis, 54, 1417–1426] and Jung, J.S., 2005 [Iterative approaches to common fixed points of nonexpansive mappings in Banach spaces. Journal of Mathematical Analysis and Applications, 302, 509–520] and many other existing literatures.