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 Generalized Mann Iterations for Approximating Fixed Points of a Family of Hemicontractions | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2008 Article ID 824607 9 pages doi 2008 824607 Research Article Generalized Mann Iterations for Approximating Fixed Points of a Family of Hemicontractions Liang-Gen Hu 1 Ti-Jun Xiao 2 and Jin Liang3 1 Department of Mathematics University of Science and Technology of China Hefei 230026 China 2 School of Mathematical Sciences Fudan University Shanghai 200433 China 3 Department of Mathematics Shanghai Jiaotong University Shanghai 200240 China Correspondence should be addressed to Jin Liang jliang@ Received 10 January 2008 Accepted 15 May 2008 Recommended by Hichem Ben-El-Mechaiekh This paper concerns common fixed points for a finite family of hemicontractions or a finite family of strict pseudocontractions on uniformly convex Banach spaces. By introducing a new iteration process with error term we obtain sufficient and necessary conditions as well as sufficient conditions for the existence of a fixed point. As one will see we derive these strong convergence theorems in uniformly convex Banach spaces and without any requirement of the compactness on the domain of the mapping. The results given in this paper extend some previous theorems. Copyright 2008 Liang-Gen Hu 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 Let X be a real Banach space and K a nonempty closed subset of X. A mapping T K K is said to be pseudocontractive see . 1 if Tx - Ty II2 x - y II2 II I - T x - I - T y 2 holds for all x y G K. T is said to be strictly pseudocontractive if for all x y G K there exists a constant k G 0 1 such that Tx - Ty II2 x - y 2 kb I - T x - I - T yỊỊ2. Denote by Fix T x G K Tx x the set of fixed points of T. A map T K K is called hemicontractive if Fix T 0 and for all x G K x G Fix T the .
