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

作者：Wang Shenghua^*; Yu Lanxiang; Guo Baohua

来源：Fixed Point Theory and Applications, 2008, 2008(1): 350483.

DOI：10.1155/2008/350483

Let K be a nonempty closed convex subset of a reflexive Banach space E with a weakly continuous dual mapping, and let {T(i)}(i=1)(infinity) be an infinite countable family of asymptotically nonexpansive mappings with the sequence {k(in)} satisfying k(in) >= 1 for each i = 1,2,..., n = 1,2,..., and lim(n-->infinity) k(in) = 1 for each i = 1,2,.... In this paper, we introduce a new implicit iterative scheme generated by {T(i)}(i=1)(infinity) and prove that the scheme converges strongly to a common fixed point of {T(i)}(i=1)(infinity), which solves some certain variational inequality.
Copyright (C) 2008 Shenghua Wang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

• 出版日期2008
• 单位华北电力大学