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 Implicit Iteration Process for Common Fixed Points of Strictly Asymptotically Pseudocontractive Mappings in Banach Spaces | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2008 Article ID 324575 12 pages doi 2008 324575 Research Article Implicit Iteration Process for Common Fixed Points of Strictly Asymptotically Pseudocontractive Mappings in Banach Spaces You Xian Tian 1 Shih-sen Chang 2 Jialin Huang 2 Xiongrui Wang 2 and J. K. Kim3 1 College of Mathematics and Physics Chongqing University of Post Telecommunications Chongqing 400065 China 2 Department of Mathematics Yibin University Yibin Sichuan 644007 China 3 Department of Mathematics Kyungnam University Masan 631-701 South Korea Correspondence should be addressed to You Xian Tian tianyx@ Received 25 May 2008 Accepted 3 September 2008 Recommended by Nanjing Huang In this paper a new implicit iteration process with errors for finite families of strictly asymptotically pseudocontractive mappings and nonexpansive mappings is introduced. By using the iterative process some strong convergence theorems to approximating a common fixed point of strictly asymptotically pseudocontractive mappings and nonexpansive mappings are proved. The results presented in the paper are new which extend and improve some recent results of Osilike et al. 2007 Liu 1996 Osilike 2004 Su and Li 2006 Gu 2007 Xu and Ori 2001 . Copyright 2008 You Xian Tian 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 and preliminaries Throughout this paper we assume that E is a real Banach space C is a nonempty closed convex subset of E E is the dual space of E and J E E is the normalized duality mapping defined by J x f e E x f x 2 f 2 x e E. Recall that a set C c E is said to be closed convex and pointed cone if it is a closed set and satisfies the following conditions 1 C C c C 2 AC c C for each A. 0 3 if x e C with x Ỷ 0 then -x C. 2 Fixed Point
