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 of Common Fixed Points for Pseudocontractive Mappings | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2008 Article ID 902985 9 pages doi 2008 902985 Research Article Convergence Theorems of Common Fixed Points for Pseudocontractive Mappings Yan Hao School of Mathematics Physics and Information Science Zhejiang Ocean University Zhoushan 316004 China Correspondence should be addressed to Yan Hao zjhaoyan@ Received 10 June 2008 Accepted 24 September 2008 Recommended by Jerzy Jezierski We consider an implicit iterative process with mixed errors for a finite family of pseudocontractive mappings in the framework of Banach spaces. Our results improve and extend the recent ones announced by many others. Copyright 2008 Yan Hao. 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 Let E be a real Banach space and let J denote the normalized duality mapping from E into 2E given by J x f e E x f x 2 Ilf II2 x e E where E denotes the dual space of E and denotes the generalized duality pairing. In the sequel we denote a single-valued normalized duality mapping by j. Throughout this paper we use F T to denote the set of fixed points of the mapping T. and denote weak and strong convergence respectively. Let K be a nonempty subset of E. For a given sequence xn c K let V .- xn denote the weak w-limit set. Recall that T K K is nonexpansive if the following inequality holds Tx - Ty x - yịị Nx y e K. T is said to be strictly pseudocontractive in the terminology of Browder and Petryshyn 1 if for all x y e K there exist A 0 and j x - y e J x - y such that Tx - Ty j x - y Ilx - y 2 - A x - y - Tx - Ty 2. 2 Fixed Point Theory and Applications T is said to be pseudocontractive if for all x y e K there exists j x - y e J x - y such that Jx - Ty j x - y Ilx - y 2. It is well known that 2 is .
