Novel Hybrid Methods for Pseudomonotone Equilibrium Problems and Common Fixed Point Problems. (3rd April 2017)

• Record Type: Journal Article
• Authors: Thuy, L. Q.; Anh, P. K.; Muu, L. D.; Hai, T. N.
• Is Part Of: Numerical functional analysis and optimization. Volume 38:Number 4(2017)
• Page Start: 443
• Page End: 465
• Publication Date: 2017-04-03
• Subjects: Armijo linesearch -- equilibrium problem -- fixed point problem -- hybrid method -- parallel splitting-up technique -- pseudomonotonicity; 47H09 -- 47H10 -- 47J25 -- 65K10 -- 65Y05 -- 90C25 -- 90C33; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2016.1254244
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: The purpose of this article is to introduce some hybrid algorithms for finding a common element of the solution sets of pseudomonotone equilibrium problems and the fixed point sets of nonexpansive mappings in real Hilbert spaces. Our algorithms combine Mann's iterative methods and Armijo line-search with parallel splitting-up and hybrid techniques. The strong convergence of the proposed algorithms are established without the assumption on the Lipschitz-type condition for the bifunctions involved.