Strong Convergence of a Hybrid Projection Algorithm for Equilibrium Problems, Variational Inequality Problems and Fixed Point Problems in a Banach Space. (25th October 2009)

• Record Type: Journal Article
• Authors: Chuayjan, Wariam; Thianwan, Sornsak
• Other Names: Reich Simeon Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2009(2009)
• Publication Date: 2009-10-25
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2009/613524
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : We introduce and study a new hybrid projection algorithm for finding a common element of the set of solutions of an equilibrium problem, the set of common fixed points of relatively quasi-nonexpansive mappings, and the set of solutions of the variational inequality for an inverse-strongly-monotone operator in a Banach space. Under suitable assumptions, we show a strong convergence theorem. Using this result, we obtain some applications in a Banach space. The results obtained in this paper extend and improve the several recent results in this area.