Fixed Point Theory and Applications
Volume 2011 (2011), Article ID 706206, 13 pages
doi:10.1155/2011/706206
Research Article

Strong Convergence Theorems of the Ishikawa Process with Errors for Strictly Pseudocontractive Mapping of Browder-Petryshyn Type in Banach Spaces

Yu-Chao Tang,1,2 Yong Cai,1 and Li-Wei Liu1

1Department of Mathematics, NanChang University, Nanchang 330031, China
2Department of Mathematics, Xi'an Jiaotong University, Xi'an 710049, China

Received 18 December 2010; Accepted 23 February 2011

Academic Editor: M. de la Sen

Copyright © 2011 Yu-Chao Tang 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.

Abstract

We prove several strong convergence theorems for the Ishikawa iterative sequence with errors to a fixed point of strictly pseudocontractive mapping of Browder-Petryshyn type in Banach spaces and give sufficient and necessary conditions for the convergence of the scheme to a fixed point of the mapping. The results presented in this work give an affirmative answer to the open question raised by Zeng et al. 2006, and generalize the corresponding result of Zeng et al. 2006, Osilike and Udomene 2001, and others.