tailieunhanh - Báo cáo hóa học: " Research Article An Iterative Method for Generalized Equilibrium Problems, Fixed Point 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 An Iterative Method for Generalized Equilibrium Problems, Fixed Point Problems and Variational Inequality Problems | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2009 Article ID 531308 20 pages doi 2009 531308 Research Article An Iterative Method for Generalized Equilibrium Problems Fixed Point Problems and Variational Inequality Problems Qing-you Liu 1 Wei-you Zeng 2 and Nan-jing Huang2 1 State Key Laboratory of Oil and Gas Reservoir Geology and Exploitation Southwest Petroleum University Chengdu Sichuan 610500 China 2 Department of Mathematics Sichuan University Chengdu Sichuan 610064 China Correspondence should be addressed to Nan-jing Huang nanjinghuang@ Received 11 January 2009 Accepted 28 May 2009 Recommended by Fabio Zanolin We introduce an iterative scheme by the viscosity approximation method for finding a common element of the set of solutions of generalized equilibrium problems the set of common fixed points of infinitely many nonexpansive mappings and the set of solutions of the variational inequality for a-inverse-strongly monotone mappings in Hilbert spaces. We give some strong-convergence theorems under mild assumptions on parameters. The results presented in this paper improve and generalize the main result of Yao et al. 2007 . Copyright 2009 Qing-you Liu 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. 1. Introduction Let C be a nonempty closed convex subset of a real Hilbert space H and let C X C R be a bifunction where R is the set of real numbers. Let w C H be a nonlinear mapping. The generalized equilibrium problem GEP for C X C R and w C H is to find u e C such that u v Wu v - u 0 Vv e C. The set of solutions for the problem is denoted by Q that is Q u e C u v Wu v - u 0 Vv e C . 2 Fixed Point Theory and Applications If w 0 in then GEP reduces to the classical equilibrium problem EP and Q is denoted by EP G that is EP G u e C