tailieunhanh - Báo cáo hóa học: "Research Article Strong Convergence of an Iterative Method for Equilibrium Problems and Variational Inequality Problems"

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 Strong Convergence of an Iterative Method for Equilibrium Problems and Variational Inequality Problems | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2009 Article ID 362191 21 pages doi 2009 362191 Research Article Strong Convergence of an Iterative Method for Equilibrium Problems and Variational Inequality Problems HongYu Li1 and HongZhi Li2 1 Department of Mathematics Tianjin Polytechnic University Tianjin 300160 China 2 Department of Mathematics Agricultural University of Hebei BaoDing 071001 China Correspondence should be addressed to HongYu Li lhy_x1976@ Received 26 August 2008 Revised 11 November 2008 Accepted 9 January 2009 Recommended by Massimo Furi We introduce an iterative method for finding a common element of the set of solutions of equilibrium problems the set of solutions of variational inequality problems and the set of fixed points of finite many nonexpansive mappings. We prove strong convergence of the iterative sequence generated by the proposed iterative algorithm to the unique solution of a variational inequality which is the optimality condition for the minimization problem. Copyright 2009 H. Li and H. Li. 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 Let H be a real Hilbert space with inner product and norm II II respectively. Suppose that C is nonempty closed convex subset of H and F is a bifunction from C X C to R where R is the set of real number. The equilibrium problem is to find a x e C such that F x y 0 Vy e C. The set of such solutions is denoted by EP f . Numerous problems in physics optimization and economics reduce to find a solution of equilibrium problem. Some methods have been proposed to solve the equilibrium problems in Hilbert space see for instance Blum and Oettli 1 Combettes and Hirstoaga 2 and Moudafi 3 . A mapping A C H is called monotone if Au - Av u - v 0. A is called relaxed u v -cocoercive if .