Tuyển tập các báo cáo nghiên cứu về sinh học được đăng trên tạp chí sinh học Journal of Biology đề tài: Research Article An Algorithm for Finding a Common Solution for a System of Mixed Equilibrium Problem, | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2010 Article ID 895907 23 pages doi 2010 895907 Research Article An Algorithm for Finding a Common Solution for a System of Mixed Equilibrium Problem Quasivariational Inclusion Problem and Fixed Point Problem of Nonexpansive Semigroup M. Liu S. S. Chang and P. Zuo Department of Mathematics Yibin University Yibin Sichuan 644007 China Correspondence should be addressed to M. Liu liuminybsc@ and S. S. Chang changss@ Received 31 March 2010 Accepted 8 June 2010 Academic Editor Vy Khoi Le Copyright 2010 M. 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. We introduce a hybrid iterative scheme for finding a common element of the set of solutions for a system of mixed equilibrium problems the set of common fixed point for nonexpansive semigroup and the set of solutions of the quasi-variational inclusion problem with multivalued maximal monotone mappings and inverse-strongly monotone mappings in Hilbert space. Under suitable conditions some strong convergence theorems are proved. Our results extend some recent results announced by some authors. 1. Introduction Throughout this paper we assume that H is a real Hilbert space and C is a nonempty closed convex subset of H. In the sequel we denote the set of fixed points of S by F S . A bounded linear operator A H H is said to be strongly positive if there exists a constant Y such that Ax x Y x 2 Vx e H. Let B H H be a single-valued nonlinear mapping and M H 2H a multivalued mapping. The so-called quasi-variational inclusion problem see Chang 1 2 is to find an u e H such that e e B u M u . 2 Journal of Inequalities and Applications A number of problems arising in structural analysis mechanics and economics can be studied in the framework of this .
