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Abstract and Applied Analysis
Volume 2012, Article ID 975981, 32 pages
http://dx.doi.org/10.1155/2012/975981
Research Article

Some Modified Extragradient Methods for Solving Split Feasibility and Fixed Point Problems

1Department of Mathematics, Shanghai Normal University, Shanghai 200234, China
2Department of Mathematics, Shanghai Normal University and Scientific Computing Key Laboratory of Shanghai Universities, Shanghai 200234, China
3Center for Fundamental Science, Kaohsiung Medical University, Kaohsiung 80708, Taiwan

Received 17 October 2012; Accepted 14 November 2012

Academic Editor: Jen-Chih Yao

Copyright © 2012 Zhao-Rong Kong 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 consider and study the modified extragradient methods for finding a common element of the solution set of a split feasibility problem (SFP) and the fixed point set of a strictly pseudocontractive mapping in the setting of infinite-dimensional Hilbert spaces. We propose an extragradient algorithm for finding an element of where is strictly pseudocontractive. It is proven that the sequences generated by the proposed algorithm converge weakly to an element of . We also propose another extragradient-like algorithm for finding an element of where is nonexpansive. It is shown that the sequences generated by the proposed algorithm converge strongly to an element of .