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 A Weak Convergence Theorem for Total Asymptotically Pseudocontractive Mappings in Hilbert Spaces | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2011 Article ID 859795 11 pages doi 2011 859795 Research Article A Weak Convergence Theorem for Total Asymptotically Pseudocontractive Mappings in Hilbert Spaces Xiaolong Qin 1 Sun Young Cho 2 and Shin Min Kang3 1 School of Mathematics and Information Sciences North China University of Water Resources and Electric Power Zhengzhou 450011 China 2 Department of Mathematics Gyeongsang National University Jinju 660-701 Republic of Korea 3 Department of Mathematics and RINS Gyeongsang National University Jinju 660-701 Republic of Korea Correspondence should be addressed to Shin Min Kang smkang@ Received 13 December 2010 Accepted 1 February 2011 Academic Editor Yeol J. Cho Copyright 2011 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. The modified Ishikawa iterative process is investigated for the class of total asymptotically pseudocontractive mappings. A weak convergence theorem of fixed points is established in the framework of Hilbert spaces. 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 II. and are denoted by strong convergence and weak convergence respectively. Let C be a nonempty closed convex subset of H and T C C a mapping. In this paper we denote the fixed point set of T by F T . T is said to be a contraction if there exists a constant a e 0 1 such that Tx - Ty a x - y x y e C. Banach contraction principle guarantees that every contractive mapping defined on complete metric spaces has a unique fixed point. T is said to be a weak contraction if Tx - Tytt Ilx - y - Ilx - y x y e C 2 Fixed Point Theory and Applications where y 0 to 0 to is a continuous and nondecreasing function .
