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 New Approximation Method for Solving Variational Inequalities and Fixed Points of Nonexpansive Mappings | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2009 Article ID 520301 16 pages doi 2009 520301 Research Article A New Approximation Method for Solving Variational Inequalities and Fixed Points of Nonexpansive Mappings Chakkrid Klin-eam and Suthep Suantai Department of Mathematics Faculty of Science Chiang Mai University Chiang Mai 50200 Thailand Correspondence should be addressed to Suthep Suantai scmti005@ Received 3 June 2009 Revised 31 August 2009 Accepted 1 November 2009 Recommended by Vy Khoi Le A new approximation method for solving variational inequalities and fixed points of nonexpansive mappings is introduced and studied. We prove strong convergence theorem of the new iterative scheme to a common element of the set of fixed points of nonexpansive mapping and the set of solutions of the variational inequality for the inverse-strongly monotone mapping which solves some variational inequalities. Moreover we apply our main result to obtain strong convergence to a common fixed point of nonexpansive mapping and strictly pseudocontractive mapping in a Hilbert space. Copyright 2009 C. Klin-eam and S. Suantai. 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 Iterative methods for nonexpansive mappings have recently been applied to solve convex minimization problems. Convex minimization problems have a great impact and influence in the development of almost all branches of pure and applied sciences. A typical problem is to minimize a quadratic function over the set of the fixed points of a nonexpansive mapping on a real Hilbert space H 1 0 x 2 Ax x - x y Vx e F S where A is a linear bounded operator F S is the fixed point set of a nonexpansive mapping S and y is a given point in H. Let H be a real Hilbert space and C be a nonempty .
