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 Some Iterative Methods for Solving Equilibrium Problems and Optimization Problems | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2010 Article ID 943275 25 pages doi 2010 943275 Research Article Some Iterative Methods for Solving Equilibrium Problems and Optimization Problems Huimin He 1 Sanyang Liu 1 and Qinwei Fan2 1 Department of Mathematics Xidian University Xi An 710071 China 2 Department of Applied Mathematics Dalian University of Technology Dalian 116024 China Correspondence should be addressed to Huimin He huiminhe@ Received 3 September 2010 Accepted 29 October 2010 Academic Editor Vijay Gupta Copyright 2010 Huimin He 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 introduce a new iterative scheme for finding a common element of the set of solutions of the equilibrium problems the set of solutions of variational inequality for a relaxed cocoercive mapping and the set of fixed points of a nonexpansive mapping. The results presented in this paper extend and improve some recent results of Ceng and Yao 2008 Yao 2007 S. Takahashi and W. Takahashi 2007 Marino and Xu 2006 Iiduka and Takahashi 2005 Su et al. 2008 and many others. 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 and convex subset of H and Pc is the metric projection of H onto c. In the following we denote by strong convergence by weak convergence and by R the real number set. Recall that a mapping S c c is called nonexpansive if Sx - Syll x - y Nx y e c. We denote by F S the set of fixed points of the mapping S. For a given nonlinear operator A consider the problem of finding u e c such that Au v - u 0 Vv e c 2 Journal of Inequalities and Applications which is called the variational inequality. For the recent applications sensitivity analysis dynamical
