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 of Cesaro Mean | Hindawi Publishing Corporation Fixed Point Theory and Applications Volume 2011 Article ID 945051 24 pages doi 2011 945051 Research Article A Viscosity of Cesaro Mean Approximation Methods for a Mixed Equilibrium Variational Inequalities and Fixed Point Problems Thanyarat Jitpeera Phayap Katchang and Poom Kumam Department of Mathematics Faculty of Science King Mongkut s University of Technology Thonburi KMUTT Bangmod Bangkok 10140 Thailand Correspondence should be addressed to Poom Kumam Received 6 September 2010 Accepted 15 October 2010 Academic Editor Qamrul Hasan Ansari Copyright 2011 Thanyarat Jitpeera 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. We introduce a new iterative method for finding a common element of the set of solutions for mixed equilibrium problem the set of solutions of the variational inequality for a -inverse-strongly monotone mapping and the set of fixed points of a family of finitely nonexpansive mappings in a real Hilbert space by using the viscosity and Cesaro mean approximation method. We prove that the sequence converges strongly to a common element of the above three sets under some mind conditions. Our results improve and extend the corresponding results of Kumam and Katchang 2009 Peng and Yao 2009 Shimizu and Takahashi 1997 and some authors. 1. Introduction Throughout this paper we assume that H is a real Hilbert space with inner product and norm are denoted by and II II respectively and let C be a nonempty closed convex subset of H. A mapping T C C is called nonexpansive if Tx - Ty x - yịị for all x y e C. We use F T to denote the set of fixed points of T that is F T x e C Tx x . It is assumed throughout the paper that T is a nonexpansive mapping such that F T f 0. Recall that a self-mapping f C C is a contraction on C if there exists
