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Báo cáo hóa học: "Research Article Hybrid Methods for Equilibrium Problems and Fixed Points Problems of a Countable Family of Relatively Nonexpansive Mappings in Banach 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 Hybrid Methods for Equilibrium Problems and Fixed Points Problems of a Countable Family of Relatively Nonexpansive Mappings in Banach Spaces | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2010 Article ID 962628 17 pages doi 10.1155 2010 962628 Research Article Hybrid Methods for Equilibrium Problems and Fixed Points Problems of a Countable Family of Relatively Nonexpansive Mappings in Banach Spaces Somyot Plubtieng and Wanna Sriprad Department of Mathematics Faculty of Science Naresuan University Phitsanulok 65000 Thailand Correspondence should be addressed to Somyot Plubtieng somyotp@nu.ac.th Received 1 August 2009 Accepted 19 November 2009 Academic Editor Tomonari Suzuki Copyright 2010 S. Plubtieng and W. Sriprad. 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. The purpose of this paper is to introduce hybrid projection algorithms for finding a common element of the set of common fixed points of a countable family of relatively nonexpansive mappings and the set of solutions of an equilibrium problem in the framework of Banach spaces. Moreover we apply our result to the problem of finding a common element of an equilibrium problem and the problem of finding a zero of a maximal monotone operator. Our result improve and extend the corresponding results announced by Takahashi and Zembayashi 2008 and 2009 and many others. 1. Introduction Let E be a real Banach space and E the dual space of E. Let C be a nonempty closed convex subset of E and f a bifunction from C X C to R where R denotes the set of real numbers. The equilibrium problem is to find p e C such that f p y 0 vy e C- 1.1 The set of solutions of 1.1 is denoted by EP f . Given a mapping T C E let f x y Tx y - x for all x y e C. Then p e EP f if and only if Tp y - p 0 for all y e C that is p is a solution of the variational inequality. Numerous problems in physics optimization and economics reduced to find a solution of 1.1 . Some methods have been proposed to .