Fixed Point Theory and Applications
Volume 2008 (2008), Article ID 350483, 10 pages
doi:10.1155/2008/350483

An implicit iterative scheme for an infinite countable family of asymptotically nonexpansive mappings in Banach spaces

Abstract

Let K be a nonempty closed convex subset of a reflexive Banach space E with a weakly continuous dual mapping, and let {Ti}i=1∞ be an infinite countable family of asymptotically nonexpansive mappings with the sequence {kin} satisfying kin≥1 for each i=1,2,…, n=1,2,…, and limn→∞kin=1 for each i=1,2,…. In this paper, we introduce a new implicit iterative scheme generated by {Ti}i=1∞ and prove that the scheme converges strongly to a common fixed point of {Ti}i=1∞, which solves some certain variational inequality.