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

An Implicit Iterative Scheme for an Infinite Countable Family of Asymptotically Nonexpansive Mappings in Banach Spaces

Shenghua Wang, Lanxiang Yu, and Baohua Guo

 School of Mathematics and Physics, North China Electric Power University, Baoding 071003, China
Received 6 May 2008; Accepted 24 August 2008

Recommended by William Kirk

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.