tailieunhanh - Báo cáo hóa học: " Research Article Weak and Strong Convergence Theorems for Asymptotically Strict Pseudocontractive Mappings in the Intermediate Sense"

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 Weak and Strong Convergence Theorems for Asymptotically Strict Pseudocontractive Mappings in the Intermediate Sense | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2010 Article ID 281070 13 pages doi 2010 281070 Research Article Weak and Strong Convergence Theorems for Asymptotically Strict Pseudocontractive Mappings in the Intermediate Sense Jing Zhao1 2 and Songnian He1 2 1 College of Science Civil Aviation University of China Tianjin 300300 China 2 Tianjin Key Laboratory For Advanced Signal Processing Civil Aviation University of China Tianjin 300300 China Correspondence should be addressed to Jing Zhao zhaojing200103@ Received 23 June 2010 Accepted 19 October 2010 Academic Editor W. A. Kirk Copyright 2010 J. Zhao and S. He. 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. We study the convergence of Ishikawa iteration process for the class of asymptotically K-strict pseudocontractive mappings in the intermediate sense which is not necessarily Lipschitzian. Weak convergence theorem is established. We also obtain a strong convergence theorem by using hybrid projection for this iteration process. Our results improve and extend the corresponding results announced by many others. 1. Introduction and Preliminaries Throughout this paper we always assume that H is a real Hilbert space with inner product and norm II . and denote weak and strong convergence respectively. Vw xn denotes the weak w-limit set of xn that is Vw xn x e H 3xnj x . Let C be a nonempty closed convex subset of H. It is well known that for every point x e H there exists a unique nearest point in C denoted by Pcx such that Ilx - Pcxll x - yịị for all y e c. Pc is called the metric projection of H onto c. Pc is a nonexpansive mapping of H onto c and satisfies x - y Pcx - Pcy Pcx - Pcy 2 Vx y e H. 2 Fixed Point Theory and Applications Let T C C be a mapping. In this paper we denote the fixed point set of T by