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 Strong Convergence of Modified Implicit Iteration Processes for Common Fixed Points of Nonexpansive Mappings | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2007 Article ID 48174 9 pages doi 2007 48174 Research Article Strong Convergence of Modified Implicit Iteration Processes for Common Fixed Points of Nonexpansive Mappings Fang Zhang and Yongfu Su Received 21 December 2006 Accepted 19 March 2007 Recommended by William Art Kirk Strong convergence theorems are obtained by hybrid method for modified composite implicit iteration process of nonexpansive mappings in Hilbert spaces. The results presented in this paper generalize and improve the corresponding results of Nakajo and Takahashi 2003 and others. Copyright 2007 F. Zhang and Y. Su. 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 Throughout this paper let H be a real Hilbert space with inner product and norm II II. Let C be a nonempty closed convex subset of H we denote by PC the metric projection from H onto C. It is known that z PC x is equivalent to z - y x - z 0 for every y e C. Recall that T C - C is nonexpansive if II Tx - Tyll x - y II for all x y e C. A point x e C is a fixed point of T provided that Tx x. Denote by F T the set of fixed points of T that is F T x e C Tx x . It is known that F T is closed and convex. Construction of fixed points of nonexpansive mappings and asymptotically nonex-pansive mappings is an important subject in the theory of nonexpansive mappings and finds application in a number of applied areas in particular in image recovery and signal processing see . 1-5 . However the sequence Tnx 0 of iterates of the mapping T at a point x e C may not converge even in the weak topology. Thus averaged iterations prevail. Indeed Mann s iterations do have weak convergence. More precisely Mann s iteration procedure is a sequence xn which is generated in the following .
