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Tuyển tập các báo cáo nghiên cứu về hóa học được đăng trên tạp chí hóa hoc quốc tế đề tài : Convergence theorems for uniformly quasi -asymptotically nonexpansive mappings, generalized equilibrium problems, and variational inequalities | Saewan and Kumam Journal of Inequalities and Applications 2011 2011 96 http www.journalofinequalitiesandapplications.eom content 2011 1 96 Journal of Inequalities and Applications a SpringerOpen Journal RESEARCH Open Access Convergence theorems for uniformly quasi- -asymptotically nonexpansive mappings generalized equilibrium problems and variational inequalities Siwaporn Saewan 1 and Room Kumam1 2 Correspondence poom. kum@kmutt.ac.th 1Department of Mathematics Faculty of Science King Mongkut s University of Technology Thonburi KMUK Bangmod Bangkok 10140 Thailand Full list of author information is available at the end of the article Springer Abstract In this article we introduce an iterative algorithm for finding a common element of the set of common fixed points of an infinite family of closed and uniformly quasi- -asymptotically nonexpansive mappings the set of the variational inequality for an a-inverse-strongly monotone operator and the set of solutions of the generalized equilibrium problems. We obtain a strong convergence theorem for the sequences generated by this process in a 2-uniformly convex and uniformly smooth Banach space. The results presented in this article improve and extend the recent results of Zegeye Nonlinear Anal. 72 2136-2146 2010 Wattanawitoon and Kumam Nonlinear Anal. Hybrid Syst. 3 1 11-20 2009 and many others. 2000 MSC 47H05 47H09 47H10. Keywords iterative algorithms inverse-strongly monotone operator variational inequality generalized equilibrium problem uniformly quasi- -asymptotically nonex-pansive mapping 1 Introduction and preliminaries Let C be a nonempty closed convex subset of a real Banach space E with and E the dual space of E. Recall that a mapping T C C is said to be L-Lipschitz continuous if Tx - Ty L x - y Vx y e C and a mapping Tis said to be nonexpansive if Tx - Ty x - y Vx y e C. A point x e C is a fixed point of T provided Tx x. Denote by F T the set of fixed points of T that is F T x e C Tx x . Let A C E be a mapping.