tailieunhanh - Báo cáo hóa học: " Research Article A General Iterative Method for Equilibrium Problems and Fixed Point Problems in Hilbert Spaces"

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 General Iterative Method for Equilibrium Problems and Fixed Point Problems in Hilbert Spaces | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2007 Article ID 95412 9 pages doi 2007 95412 Research Article A General Iterative Method for Equilibrium Problems and Fixed Point Problems in Hilbert Spaces Meijuan Shang Yongfu Su and Xiaolong Qin Received 14 May 2007 Revised 15 August 2007 Accepted 18 September 2007 Recommended by Hichem Ben-El-Mechaiekh We introduce a general 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. Our results improve and extend the corresponding ones announced by S. Takahashi and W. Takahashi in 2007 Marino and Xu in 2006 Combettes and Hirstoaga in 2005 and many others. Copyright 2007 Meijuan Shang 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 nonempty closed convex subset of H. Recall that a mapping s of C into itself is called nonexpansive if Sx - Sy 11 x - y II for all x y e C. We denote by F S the set of fixed points of s. Let B be a bifunction of C X C into R where R is the set of real numbers. The equilibrium problem for B C X C R is to find x e C such that B x y 0 Vy e C. The set of solutions of is denoted by EP B . Give a mapping T C H let B x y Tx y - x for all x y e C. Then z e EP B if and only if Tz y - z 0 for all y e C that is z is a solution of the variational inequality. Numerous problems in physics optimization and economics reduce to find a solution of . Some methods have been proposed to solve the equilibrium problem see for instance 1 2 . Recently Combettes and Hirstoaga 1 introduced an iterative scheme of finding the best approximation to the initial data when EP B is nonempty and proved a .