tailieunhanh - báo cáo hóa học:" Research Article Convergence Theorems on Asymptotically 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 Convergence Theorems on Asymptotically Pseudocontractive Mappings in the Intermediate Sense | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2010 Article ID 186874 14 pages doi 2010 186874 Research Article Convergence Theorems on Asymptotically Pseudocontractive Mappings in the Intermediate Sense Xiaolong Qin 1 Sun Young Cho 2 and Jong Kyu Kim3 1 Department of Mathematics Hangzhou Normal University Hangzhou 310036 China 2 Department of Mathematics Gyeongsang National University Jinju 660-701 South Korea 3 Department of Mathematics Education Kyungnam University Masan 631-701 South Korea Correspondence should be addressed to Jong Kyu Kim jongkyuk@ Received 15 October 2009 Revised 8 January 2010 Accepted 23 February 2010 Academic Editor Tomonari Suzuki Copyright 2010 Xiaolong Qin 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. A new nonlinear mapping is introduced. The convergence of Ishikawa iterative processes for the class of asymptotically pseudocontractive mappings in the intermediate sense is studied. Weak convergence theorems are established. A strong convergence theorem is also established without any compact assumption by considering the so-called hybrid projection methods. 1. Introduction and Preliminaries Throughout this paper we always assume that H is a real Hilbert space whose inner product and norm are denoted by and II . The symbols and are denoted by strong convergence and weak convergence respectively. Vw xn x 3xni x denotes the weak w-limit set of xn . Let C be a nonempty closed and convex subset of H and T C C a mapping. In this paper we denote the fixed point set of T by F T . Recall that T is said to be nonexpansive if Tx - Ty x - y Nx y e C. T is said to be asymptotically nonexpansive if there exists a sequence kn c 1 to with kn 1 as n to such that Tnx - Tnytf kn x - yịị n 1 x y e C. 2 Fixed Point Theory and .