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 Hybrid Algorithm for a System of Mixed Equilibrium Problems, Fixed Point Problems for Nonexpansive Semigroup, and Variational Inclusion Problem | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2011 Article ID 217407 27 pages doi 2011 217407 Research Article A New Hybrid Algorithm for a System of Mixed Equilibrium Problems Fixed Point Problems for Nonexpansive Semigroup and Variational Inclusion Problem Thanyarat Jitpeera and Poom Kumam Department of Mathematics Faculty of Science King Mongkut s University of Technology Thonburi KMUTT Bangmod Bangkok 10140 Thailand Correspondence should be addressed to Poom Kumam Received 14 December 2010 Accepted 15 January 2011 Academic Editor Jen Chih Yao Copyright 2011 T. Jitpeera and P. Kumam. 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. The purpose of this paper is to consider a shrinking projection method for finding the common element of the set of common fixed points for nonexpansive semigroups the set of common fixed points for an infinite family of a -strict pseudocontraction the set of solutions of a system of mixed equilibrium problems and the set of solutions of the variational inclusion problem. Strong convergence of the sequences generated by the proposed iterative scheme is obtained. The results presented in this paper extend and improve some well-known results in the literature. 1. Introduction Throughout this paper we assume that H be a real Hilbert space with inner product and norm II II and let C be a nonempty closed convex subset of H. We denote weak convergence and strong convergence by notations and respectively. Let I Fk ker be a countable family of bifunctions from C X C to R where R is the set of real numbers and r is an arbitrary index set. Let f C Ru i v. be a proper extended real-valued function. The system of mixed equilibrium problems is to find x e C such that Fk x y y y q x Nk e r Vy e C. The set of solutions of is .
