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 Hybrid-Extragradient Scheme for System of Equilibrium Problems, Nonexpansive Mappings, and Monotone Mappings | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2011 Article ID 232163 15 pages doi 2011 232163 Research Article A Hybrid-Extragradient Scheme for System of Equilibrium Problems Nonexpansive Mappings and Monotone Mappings Jian-Wen Peng 1 Soon-Yi Wu 2 and Gang-Lun Fan2 1 School of Mathematics Chongqing Normal University Chongqing 400047 China 2 Department of Mathematics National Cheng Kung University Tainan 701 Taiwan Correspondence should be addressed to Jian-Wen Peng jwpeng6@ Received 21 October 2010 Accepted 24 November 2010 Academic Editor Jen Chih Yao Copyright 2011 Jian-Wen Peng 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 based on both hybrid method and extragradient method for finding a common element of the solutions set of a system of equilibrium problems the fixed points set of a nonexpansive mapping and the solutions set of a variational inequality problems for a monotone and fc-Lipschitz continuous mapping in a Hilbert space. Some convergence results for the iterative sequences generated by these processes are obtained. The results in this paper extend and improve some known results in the literature. 1. Introduction In this paper we always assume that H is a real Hilbert space with inner product and induced norm II II and C is a nonempty closed convex subset of H S C C is a nonexpansive mapping that is Sx - Sy x - y for all x y e C PC denotes the metric projection of H onto C and Fix S denotes the fixed points set of S. Let Ffc fcer be a countable family of bifunctions from C X C to R where R is the set of real numbers. Combettes and Hirstoaga 1 introduced the following system of equilibrium problems finding x e C such that Vfc e r Vy e C Ffc x y 0 where r is an arbitrary index set. If r is a .
