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 General Iterative Method for Solving the Variational Inequality Problem and Fixed Point Problem of an Infinite Family of Nonexpansive Mappings in Hilbert Spaces | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2009 Article ID 369215 23 pages doi 2009 369215 Research Article A General Iterative Method for Solving the Variational Inequality Problem and Fixed Point Problem of an Infinite Family of Nonexpansive Mappings in Hilbert Spaces Rabian Wangkeeree and Uthai Kamraksa Department of Mathematics Faculty of Science Naresuan University Phitsanulok 65000 Thailand Correspondence should be addressed to Rabian Wangkeeree rabianw@ Received 3 November 2008 Accepted 16 January 2009 Recommended by Anthony Lau We introduce an iterative scheme for finding a common element of the set of common fixed points of a family of infinitely nonexpansive mappings and the set of solutions of the variational inequality for an inverse-strongly monotone mapping in a Hilbert space. Under suitable conditions some strong convergence theorems for approximating a common element of the above two sets are obtained. As applications at the end of the paper we utilize our results to study the problem of finding a common element of the set of fixed points of a family of infinitely nonexpansive mappings and the set of fixed points of a finite family of fc-strictly pseudocontractive mappings. The results presented in the paper improve some recent results of Qin and Cho 2008 . Copyright 2009 R. Wangkeeree and U. Kamraksa. 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 Throughout this paper we always assume that H is a real Hilbert space with inner product and norm II II respectively C is a nonempty closed convex subset of H and Pc is the metric projection of H onto c. In the following we denote by strong convergence and by weak convergence. Recall that a mapping T c c is called nonexpansive if Tu - Tv u - v Nu v e c. We denote by P T the set
