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 Iterative Algorithm for Fixed-Point Problems, Variational Inequality Problems, and Mixed Equilibrium Problems | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2008 Article ID 417089 15 pages doi 2008 417089 Research Article A New Hybrid Iterative Algorithm for Fixed-Point Problems Variational Inequality Problems and Mixed Equilibrium Problems Yonghong Yao 1 Yeong-Cheng Liou 2 and Jen-Chih Yao3 1 Department of Mathematics Tianjin Polytechnic University Tianjin 300160 China 2 Department of Information Management Cheng Shiu University Kaohsiung 833 Taiwan 3 Department of Applied Mathematics National Sun Yat-Sen University Kaohsiung 804 Taiwan Correspondence should be addressed to Jen-Chih Yao yaojc@ Received 29 August 2007 Accepted 6 February 2008 Recommended by Tomonari Suzuki We introduce a new hybrid iterative algorithm for finding a common element of the set of fixed points of an infinite family of nonexpansive mappings the set of solutions of the variational inequality of a monotone mapping and the set of solutions of a mixed equilibrium problem. This study proves a strong convergence theorem by the proposed hybrid iterative algorithm which solves fixed-point problems variational inequality problems and mixed equilibrium problems. Copyright 2008 Yonghong Yao 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. Recall that a mapping f C C is called contractive if there exists a constant a G 0 1 such that f x - f y a x- y for all x y G C. A mapping T C C is said to be nonexpansive if Tx- Ty x- yịị for all x y G C. Denote the set of fixed points of T by F T . Let ọ C R be a real-valued function and 0 C X C R be an equilibrium bifunction that is 0 u u 0 for each u G C. The mixed equilibrium problem for short MEP is to find x G C such that MEP 0 x y ọy - ọ x 0 Vy G C. In .
