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 Finding Common Solutions of a Variational Inequality, a General System of Variational Inequalities, and a Fixed-Point Problem via a Hybrid Extragradient Method | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2011 Article ID 626159 22 pages doi 2011 626159 Research Article Finding Common Solutions of a Variational Inequality a General System of Variational Inequalities and a Fixed-Point Problem via a Hybrid Extragradient Method Lu-Chuan Ceng 1 Sy-Ming Guu 2 and Jen-Chih Yao3 1 Department of Mathematics Shanghai Normal University Scientific Computing Key Laboratory of Shanghai Universities Shanghai 200234 China 2 Department of Business Administration College of Management Yuan-Ze University Taoyuan Hsien Chung-Li City 330 Taiwan 3 Department of Applied Mathematics National Sun Yat-Sen University Kaohsiung 804 Taiwan Correspondence should be addressed to Sy-Ming Guu iesmguu@ Received 25 September 2010 Accepted 20 December 2010 Academic Editor Jong Kim Copyright 2011 Lu-Chuan Ceng 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. We propose a hybrid extragradient method for finding a common element of the solution set of a variational inequality problem the solution set of a general system of variational inequalities and the fixed-point set of a strictly pseudocontractive mapping in a real Hilbert space. Our hybrid method is based on the well-known extragradient method viscosity approximation method and Mann-type iteration method. By constrasting with other methods our hybrid approach drops the requirement of boundedness for the domain in which various mappings are defined. Furthermore under mild conditions imposed on the parameters we show that our algorithm generates iterates which converge strongly to a common element of these three problems. 1. Introduction Let H be a real Hilbert space with inner product and norm II II. Let C be a nonempty closed convex subset of H and S C C be a self-mapping on C. We .
