Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 354202, 19 pages
doi:10.1155/2010/354202
Research Article

Strong Convergence Theorems of a New General Iterative Process with Meir-Keeler Contractions for a Countable Family of 𝜆 𝑖 -Strict Pseudocontractions in 𝑞 -Uniformly Smooth Banach Spaces

Yanlai Song and Changsong Hu

Department of Mathematics, Hubei Normal University, Huangshi 435002, China

Received 9 August 2010; Revised 2 October 2010; Accepted 14 November 2010

Academic Editor: Mohamed Amine Khamsi

Copyright © 2010 Yanlai Song and Changsong Hu. 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 introduce a new iterative scheme with Meir-Keeler contractions for strict pseudocontractions in 𝑞 -uniformly smooth Banach spaces. We also discuss the strong convergence theorems for the new iterative scheme in 𝑞 -uniformly smooth Banach space. Our results improve and extend the corresponding results announced by many others.