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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 Approximation Methods for Common Fixed Points of Mean Nonexpansive Mapping in Banach Spaces | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2008 Article ID 471532 7 pages doi 10.1155 2008 471532 Research Article Approximation Methods for Common Fixed Points of Mean Nonexpansive Mapping in Banach Spaces Zhaohui Gu1 and Yongjin Li2 1 Department of Foundation Guangdong Finance and Economics College Guangzhou 510420 China 2 Institute of Logic and Cognition Department of Mathematics Sun Yat-Sen University Guangzhou 510275 China Correspondence should be addressed to Yongjin Li stslyj@mail.sysu.edu.cn Received 17 October 2007 Accepted 2 January 2008 Recommended by Tomonari Suzuki Let X be a uniformly convex Banach space and let S T be a pair of mean nonexpansive mappings. In this paper it is proved that the sequence of Ishikawa iterations associated with S and T converges to the common fixed point of S and T. Copyright 2008 Z. Gu and Y. Li. 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 and preliminaries Let X be a Banach space and let S T be mappings from X to X. The pair of mean nonexpansive mappings was introduced by Bose in 1 llSx - TyH a x - yH b Hx - Sx y - Ty c Hx - Tyti y - Sxl 1.1 for all x y G X a b c G 0 1 a 2b 2c 1. The Ishikawa iteration sequence xn of S and T was defined by yn - C1 fin xn finSxn 1.2 Xn 1 1 an xn anTy n where x0 G X an fn G 0 1 . The recursion formulas 1.2 were first introduced in 1994 by Rashwan and Saddeek 2 in the framework of Hilbert spaces. In recent years several authors see 2-6 have studied the convergence of iterations to a common fixed point for a pair of mappings. Rashwan has studied the convergence of Mann iterations to a common fixed point see 5 and proved that the Ishikawa iterations converge 2 Fixed Point Theory and Applications to a unique common fixed point in Hilbert spaces see 2 . Recently Ciric has proved that .
