tailieunhanh - báo cáo hóa học:" Research Article Strong Convergence Theorems by Hybrid Methods for Strict Pseudocontractions and Equilibrium Problems"

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 Strong Convergence Theorems by Hybrid Methods for Strict Pseudocontractions and Equilibrium Problems | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2010 Article ID 528307 13 pages doi 2010 528307 Research Article Strong Convergence Theorems by Hybrid Methods for Strict Pseudocontractions and Equilibrium Problems Peichao Duan and Jing Zhao College of Science Civil Aviation University of China Tianjin 300300 China Correspondence should be addressed to Peichao Duan pcduancauc@ Received 21 December 2009 Accepted 9 May 2010 Academic Editor Massimo Furi Copyright 2010 P. Duan and J. Zhao. 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. Let Si 1 be N strict pseudocontractions defined on a closed convex subset C of a real Hilbert space H. Consider the problem of finding a common element of the set of fixed point of these mappings and the set of solutions of an equilibrium problem with the parallel and cyclic algorithms. In this paper we propose new iterative schemes for solving this problem and prove these schemes converge strongly by hybrid methods. 1. Introduction Let H be a real Hilbert space and let C be a nonempty closed convex subset of H. Let f be a bifunction from C X C to R where R is the set of real numbers. The equilibrium problem for f C X C R is to find x e C such that f x ỳ 0 M for all ỳ e C. The set of such solutions is denoted by EP f . A mapping S of C is said to be a K-strict pseudocontraction if there exists a constant K e 0 1 such that IISx- Sỳ 2 x - ỳ 2 k I - S x - I - S ỳ 2 L2 for all x ỳ e C see 1 . We denote the set of fixed points of S by F S . F S x e C Sx x . 2 Fixed Point Theory and Applications Note that the class of strict pseudocontractions strictly includes the class of nonexpansive mappings which are mapping S on C such that Sx - Sy x - y for all x y e C. That is S is nonexpansive if and only if S is a 0-strict pseudocontraction. .