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Báo cáo hóa học: " Research Article Convergence Theorems Concerning Hybrid Methods for Strict Pseudocontractions and Systems of 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 Convergence Theorems Concerning Hybrid Methods for Strict Pseudocontractions and Systems of Equilibrium Problems | Hindawi Publishing Corporation Journal of Inequalities and Applications Volume 2010 Article ID 396080 14 pages doi 10.1155 2010 396080 Research Article Convergence Theorems Concerning Hybrid Methods for Strict Pseudocontractions and Systems of Equilibrium Problems Peichao Duan College of Science Civil Aviation University of China Tianjin 300300 China Correspondence should be addressed to Peichao Duan pcduancauc@126.com Received 23 May 2010 Revised 23 August 2010 Accepted 26 August 2010 Academic Editor S. Reich Copyright 2010 Peichao Duan. 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 f 1 be N strict pseudo-contractions defined on a closed and convex subset C of a real Hilbert space H. We consider the problem of finding a common element of fixed point set of these mappings and the solution set of a system of equilibrium problems by parallel and cyclic algorithms. In this paper new iterative schemes are proposed for solving this problem. Furthermore we prove that these schemes converge strongly by hybrid methods. The results presented in this paper improve and extend some well-known results in the literature. 1. Introduction Let H be a real Hilbert space with inner product and norm II II. Let C be a nonempty closed and convex subset of H. Let Fk be a countable family of bifunctions from C X C to R where R is the set of real numbers. Combettes and Hirstoaga 1 considered the following system of equilibrium problems finding x e C such that Fk x y 0 Vk e r Vy e C 1.1 where r is an arbitrary index set. If r is a singleton then problem 1.1 becomes the following equilibrium problem finding x e C such that F x y 0 Vy e C. 1.2 The solution set of 1.2 is denoted by EP F . 2 Journal of Inequalities and Applications A mapping S of C is said to be a K-strict pseudocontraction if there exists a constant K e 0 1