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Báo cáo hóa học: "Research Article Convergence Theorems for the Unique Common Fixed Point of a Pair of Asymptotically Nonexpansive Mappings in Generalized Convex Metric Space"

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 the Unique Common Fixed Point of a Pair of Asymptotically Nonexpansive Mappings in Generalized Convex Metric Space | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2010 Article ID 281890 6 pages doi 10.1155 2010 281890 Research Article Convergence Theorems for the Unique Common Fixed Point of a Pair of Asymptotically Nonexpansive Mappings in Generalized Convex Metric Space Chao Wang 1 Jin Li 2 and Daoli Zhu2 1 Department of Applied Mathematics Tongji University Shanghai 200092 China 2 Department of Management Science School of Management Fudan University Shanghai 200433 China Correspondence should be addressed to Chao Wang 0810102006@tongji.edu.cn and Jin Li 071025019@fudan.edu.cn Received 21 September 2009 Accepted 13 December 2009 Academic Editor Tomonari Suzuki Copyright 2010 Chao Wang 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. Let X be a generalized convex metric space and let S T be a pair of asymptotically nonexpansive mappings. In this paper we will consider an Ishikawa type iteration process with errors to approximate the unique common fixed point of S and T. 1. Introduction and Preliminaries Let X d be a metric space S T X X a pair of asymptotically nonexpansive mappings if there exists a b c e 0 1 a 2b 2c 1 such that d Snx Tny ad x y b d x Snx d y Tny c d x Tny d y Snx for all x y e X n 1. Bose 1 first defined a pair of mean nonexpansive mappings in Banach space that is IISx - Tyịị allx - y b llx - Sxll y - Ty c x - Ty y - Sxl Ơ.1 let n 1 in and then they proved several convergence theorems for commom fixed points of mean nonexpansive mappings. Gu and Li 2 also studied the same problem they 2 Fixed Point Theory and Applications considered the Ishikawa iteration process to approximate the common fixed point of mean nonexpansive mappings in uniformly convex Banach space. Takahashi 3 first introduced a notion of convex metric space which is more general space and each linear