Đang chuẩn bị nút TẢI XUỐNG, xin hãy chờ
Tải xuống
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 Convergence Theorems for Common Fixed Points of Nonself Asymptotically Quasi-Non-Expansive Mappings | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2008 Article ID 428241 11 pages doi 10.1155 2008 428241 Research Article Convergence Theorems for Common Fixed Points of Nonself Asymptotically Quasi-Non-Expansive Mappings Chao Wang and Jinghao Zhu Department of Applied Mathematics Tongji University Shanghai 200092 China Correspondence should be addressed to Chao Wang wangchaoxj20002000@yahoo.com.cn Received 1 April 2008 Revised 12 June 2008 Accepted 19 July 2008 Recommended by Simeon Reich We introduce a new three-step iterative scheme with errors. Several convergence theorems of this scheme are established for common fixed points of nonself asymptotically quasi-non-expansive mappings in real uniformly convex Banach spaces. Our theorems improve and generalize recent known results in the literature. Copyright 2008 C. Wang and J. Zhu. 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 Let K be a nonempty closed convex subset of real normed linear space E. Recall that a mapping T K . K is called asymptotically nonexpansive if there exists a sequence rn c 0 to with lim .TO rn 0 such that Tnx - Tny 1 rn x - y for all x y e K and n 1. Moreover it is uniformly L-Lipschitzian if there exists a constant L 0 such that Tnx - Tny L x - y for all x y e K and each n 1. Denote and define by F T x e K Tx x the set of fixed points of T. Suppose F T 0. A mapping T is called asymptotically quasi-non-expansive if there exists a sequence rn c 0 to with limn.TO rn 0 such that Tnx - p 1 rn x - p for all x y e K p e F T and n 1. It is clear from the above definitions that an asymptotically nonexpansive mapping must be uniformly L-Lipschitzian as well as asymptotically quasi-non-expansive but the converse does not hold. Iterative technique for asymptotically nonexpansive self-mapping in .