Báo cáo hóa học: "Research Article A Viscosity Approximation Method for Finding Common Solutions of Variational Inclusions"

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 Viscosity Approximation Method for Finding Common Solutions of Variational Inclusions | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2009 Article ID 567147 20 pages doi 2009 567147 Research Article A Viscosity Approximation Method for Finding Common Solutions of Variational Inclusions Equilibrium Problems and Fixed Point Problems in Hilbert Spaces Somyot Plubtieng1 2 and Wanna Sriprad1 2 1 Department of Mathematics Faculty of Science Naresuan University Phitsanulok 65000 Thailand 2 PERDO National Centre of Excellence in Mathematics Faculty of Science Mahidol University Bangkok 10400 Thailand Correspondence should be addressed to Somyot Plubtieng somyotp@ Received 12 February 2009 Accepted 18 May 2009 Recommended by William A. Kirk We introduce an iterative method for finding a common element of the set of common fixed points of a countable family of nonexpansive mappings the set of solutions of a variational inclusion with set-valued maximal monotone mapping and inverse strongly monotone mappings and the set of solutions of an equilibrium problem in Hilbert spaces. Under suitable conditions some strong convergence theorems for approximating this common elements are proved. The results presented in the paper improve and extend the main results of J. W. Peng et al. 2008 and many others. Copyright 2009 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. 1. Introduction Let H be a real Hilbert space whose inner product and norm are denoted by and II II respectively. Let C be a nonempty closed convex subset of H and let F be a bifunction of C X C into 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 y 0 Vy e C. The set of solutions of is denoted by EP F . Recently Combettes and Hirstoaga 1 introduced an iterative scheme of finding the best approximation to the .

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