tailieunhanh - Báo cáo hóa học: " Research Article Convergence Theorem for Equilibrium Problems and Fixed Point Problems of Infinite Family of Nonexpansive Mappings"

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 Convergence Theorem for Equilibrium Problems and Fixed Point Problems of Infinite Family of Nonexpansive Mappings | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2007 Article ID 64363 12 pages doi 2007 64363 Research Article Convergence Theorem for Equilibrium Problems and Fixed Point Problems of Infinite Family of Nonexpansive Mappings Yonghong Yao Yeong-Cheng Liou and Jen-Chih Yao Received 17 March 2007 Accepted 20 August 2007 Recommended by Billy E. Rhoades We introduce an iterative scheme for finding a common element of the set of solutions of an equilibrium problem and the set of common fixed points of infinite nonexpan-sive mappings in a Hilbert space. We prove a strong-convergence theorem under mild assumptions on parameters. Copyright 2007 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 H be a real Hilbert space and let C be a nonempty closed convex subset of H. Let h C X C R be an equilibrium bifunction that is h u u 0 for every u e C. Then one can define the equilibrium problem that is to find an element u e C such that EP h h u v 0 Vv e C. Denote the set of solutions of EP h by SEP h . This problem contains fixed point problems optimization problems variational inequality problems and Nash equilibrium problems as special cases see 1 . Some methods have been proposed to solve the equilibrium problem please consult 2-4 . Recently Combettes and Hirstoaga 2 introduced an iterative scheme of finding the best approximation to the initial data when SEP h 0 and proved a strong convergence theorem. Motivated by the idea of Combettes and Hirstoaga very recently Takahashi and Takahashi 4 introduced a new iterative scheme by the viscosity approximation method for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a nonexpansive mapping in a Hilbert space. Their results extend and 2 Fixed