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 Some Characterizations for a Family of Nonexpansive Mappings and Convergence of a Generated Sequence to Their Common Fixed Poin | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2010 Article ID 732872 16 pages doi 2010 732872 Research Article Some Characterizations for a Family of Nonexpansive Mappings and Convergence of a Generated Sequence to Their Common Fixed Point Yasunori Kimura1 and Kazuhide Nakajo2 1 Department of Mathematical and Computing Sciences Tokyo Institute of Technology O-okayama Meguro-ku Tokyo 152-8552 Japan 2 Faculty of Engineering Tamagawa University Tamagawa-Gakuen Machida-shi Tokyo 194-8610 Japan Correspondence should be addressed to Yasunori Kimura yasunori@ Received 7 October 2009 Accepted 19 October 2009 Academic Editor Anthony To Ming Lau Copyright 2010 Y. Kimura and K. Nakajo. 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. Motivated by the method of Xu 2006 and Matsushita and Takahashi 2008 we characterize the set of all common fixed points of a family of nonexpansive mappings by the notion of Mosco convergence and prove strong convergence theorems for nonexpansive mappings and semigroups in a uniformly convex Banach space. 1. Introduction Let C be a nonempty bounded closed convex subset of a Banach space and T C C a nonexpansive mapping that is T satisfies Tx - Ty x - y for any x y e C and consider approximating a fixed point of T. This problem has been investigated by many researchers and various types of strong convergent algorithm have been established. For implicit algorithms see Browder 1 Reich 2 Takahashi and Ueda 3 and others. For explicit iterative schemes see Halpern 4 Wittmann 5 Shioji and Takahashi 6 and others. Nakajo and Takahashi 7 introduced a hybrid type iterative scheme by using the metric projection and recently Takahashi et al. 8 established a modified type of this projection method also known as the shrinking projection method. Let us
