Hybrid Proximal-Type Algorithms for Generalized Equilibrium Problems, Maximal Monotone Operators, and Relatively Nonexpansive Mappings. (2nd November 2010)

• Record Type: Journal Article
• Authors: Zeng, Lu-Chuan; Ansari, Q. H.; Al-Homidan, S.
• Other Names: Yao Jen Chih Academic Editor.
• Is Part Of: Fixed point theory and applications. Volume 2011(2011)
• Publication Date: 2010-11-02
• Subjects: Fixed point theory -- Periodicals; Mappings (Mathematics) -- Periodicals; 515.7248
• DOI: 10.1155/2011/973028
• Languages: English
• ISSNs: 1687-1812

Abstract

Abstract : The purpose of this paper is to introduce and consider new hybrid proximal-type algorithms for finding a common element of the setEP of solutions of a generalized equilibrium problem, the setF ( S ) of fixed points of a relatively nonexpansive mappingS, and the setT − 1 0 of zeros of a maximal monotone operatorT in a uniformly smooth and uniformly convex Banach space. Strong convergence theorems for these hybrid proximal-type algorithms are established; that is, under appropriate conditions, the sequences generated by these various algorithms converge strongly to the same point inEP ∩ F ( S ) ∩ T − 1 0 . These new results represent the improvement, generalization, and development of the previously known ones in the literature.