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Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Strong Convergence of Monotone Hybrid Algorithm for Hemi-Relatively Nonexpansive Mappings | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2008 Article ID 284613 8 pages doi 10.1155 2008 284613 Research Article Strong Convergence of Monotone Hybrid Algorithm for Hemi-Relatively Nonexpansive Mappings Yongfu Su 1 Dongxing Wang 1 and Meijuan Shang1 2 1 Department of Mathematics Tianjin Polytechnic University Tianjin 300160 China 2 Department of Mathematics Shijiazhuang University Shijiazhuang 050035 China Correspondence should be addressed to Yongfu Su suyongfu@tjpu.edu.cn Received 1 June 2007 Revised 5 September 2007 Accepted 16 October 2007 Recommended by Simeon Reich The purpose of this article is to prove strong convergence theorems for fixed points of closed hemi-relatively nonexpansive mappings. In order to get these convergence theorems the monotone hybrid iteration method is presented and is used to approximate those fixed points. Note that the hybrid iteration method presented by S. Matsushita and W. Takahashi can be used for relatively nonexpansive mapping but it cannot be used for hemi-relatively nonexpansive mapping. The results of this paper modify and improve the results of S. Matsushita and W. Takahashi 2005 and some others. Copyright 2008 Yongfu Su 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. 1. Introduction In 2005 Shin-ya Matsushita and Wataru Takahashi 1 proposed the following hybrid iteration method it is also called the CQ method with generalized projection for relatively nonexpan-sive mapping T in a Banach space E x0 G C chosen arbitrarily yn f anfxn 1 an fTxn Cn z G C ộ z yn ộ z Xn 1.1 Qn z G C Xn - Z fX0 - fXn 0 Xn 1 n xo . CnOQn They proved the following convergence theorem. 2 Fixed Point Theory and Applications Theorem 1.1 MT . Let E be a uniformly convex and uniformly smooth real Banach space let C be a nonempty closed and convex .
