Strong Convergence Theorem by a New Hybrid Method for Equilibrium Problems and Relatively Nonexpansive Mappings. (3rd February 2008)

• Record Type: Journal Article
• Authors: Takahashi, Wataru; Zembayashi, Kei
• Other Names: Reich Simeon Academic Editor.
• Is Part Of: Fixed point theory and applications. Volume 2008(2008)
• Publication Date: 2008-02-03
• Subjects: Fixed point theory -- Periodicals; Mappings (Mathematics) -- Periodicals; 515.7248
• DOI: 10.1155/2008/528476
• Languages: English
• ISSNs: 1687-1812

Abstract

Abstract : We prove a strong convergence theorem for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a relatively nonexpansive mapping in a Banach space by using a new hybrid method. Using this theorem, we obtain two new results for finding a solution of an equilibrium problem and a fixed point of a relatively nonexpnasive mapping in a Banach space.