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Abstract and Applied Analysis
Volume 2011 (2011), Article ID 745451, 19 pages
http://dx.doi.org/10.1155/2011/745451
Research Article

Weak Convergence of the Projection Type Ishikawa Iteration Scheme for Two Asymptotically Nonexpansive Nonself-Mappings

School of Science, University of Phayao, Phayao 56000, Thailand

Received 31 May 2011; Revised 26 August 2011; Accepted 30 August 2011

Academic Editor: Victor M. Perez Garcia

Copyright © 2011 Tanakit Thianwan. 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.

Abstract

We study weak convergence of the projection type Ishikawa iteration scheme for two asymptotically nonexpansive nonself-mappings in a real uniformly convex Banach space 𝐸 which has a Fréchet differentiable norm or its dual 𝐸 has the Kadec-Klee property. Moreover, weak convergence of projection type Ishikawa iterates of two asymptotically nonexpansive nonself-mappings without any condition on the rate of convergence associated with the two maps in a uniformly convex Banach space is established. Weak convergence theorem without making use of any of the Opial's condition, Kadec-Klee property, or Fréchet differentiable norm is proved. Some results have been obtained which generalize and unify many important known results in recent literature.