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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 Weak and Strong Convergence Theorems for Nonexpansive Mappings in Banach Spaces | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2008 Article ID 751383 7 pages doi 10.1155 2008 751383 Research Article Weak and Strong Convergence Theorems for Nonexpansive Mappings in Banach Spaces Jing Zhao 1 Songnian He 1 and Yongfu Su2 1 College of Science Civil Aviation University of China Tianjin 300300 China 2 Department of Mathematics Tianjin Polytechnic University Tianjin 300160 China Correspondence should be addressed to Jing Zhao zhaojing200103@163.com Received 25 August 2007 Accepted 16 December 2007 Recommended by Tomonari Suzuki The purpose of this paper is to introduce two implicit iteration schemes for approximating fixed points of nonexpansive mapping T and a finite family of nonexpansive mappings Tj respectively in Banach spaces and to prove weak and strong convergence theorems. The results presented in this paper improve and extend the corresponding ones of H.-K. Xu and R. Ori 2001 Z. Opial 1967 and others Copyright 2008 Jing Zhao 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 and preliminaries Let E be a real Banach space K a nonempty closed convex subset of E and T K K a mapping. We use F T to denote the set of fixed points of T that is F T x G K Tx x . T is called nonexpansive if Tx - Ty x - yII for all x y G K. In this paper and denote weak and strong convergence respectively. co A denotes the closed convex hull of A where A is a subset of E. In 2001 Xu and Ori 1 introduced the following implicit iteration scheme for common fixed points of a finite family of nonexpansive mappings Tj 1 in Hilbert spaces xn anxn-1 1 aTT Tnxn n 1 1.1 where Tn Tn mod N and they proved weak convergence theorem. In this paper we introduce a new implicit iteration scheme xn anxn-1 ftnTxn-1 ỴnTxn n 1 1.2 2 Fixed Point Theory and Applications for fixed .
