Strong Convergence Theorem by Monotone Hybrid Algorithm for Equilibrium Problems, Hemirelatively Nonexpansive Mappings, and Maximal Monotone Operators. (4th January 2009)

• Record Type: Journal Article
• Authors: Cheng, Yun; Tian, Ming
• Other Names: Takahashi Wataru Academic Editor.
• Is Part Of: Fixed point theory and applications. Volume 2008(2008)
• Publication Date: 2009-01-04
• Subjects: Fixed point theory -- Periodicals; Mappings (Mathematics) -- Periodicals; 515.7248
• DOI: 10.1155/2008/617248
• Languages: English
• ISSNs: 1687-1812

Abstract

Abstract : We introduce a new hybrid iterative algorithm for finding a common element of the set of fixed points of hemirelatively nonexpansive mappings and the set of solutions of an equilibrium problem and for finding a common element of the set of zero points of maximal monotone operators and the set of solutions of an equilibrium problem in a Banach space. Using this theorem, we obtain three new results for finding a solution of an equilibrium problem, a fixed point of a hemirelatively nonexpnasive mapping, and a zero point of maximal monotone operators in a Banach space.