Inertial methods for fixed point problems and zero point problems of the sum of two monotone mappings. (4th May 2019)

• Record Type: Journal Article
• Authors: Thong, Duong Viet; Vinh, Nguyen The
• Is Part Of: Optimization. Volume 68:Number 5(2019)
• Page Start: 1037
• Page End: 1072
• Publication Date: 2019-05-04
• Subjects: Mann algorithm -- viscosity method -- inertial method -- forward-backward splitting method -- fixed point problem; 65Y05 -- 65K15 -- 68W10 -- 47H05 -- 47H10; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2019.1573240
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: The purpose of this paper is to investigate the problem of finding a common element of the set of zero points of the sum of two operators and the fixed point set of a quasi-nonexpansive mapping. We introduce modified forward-backward splitting methods based on the so-called inertial forward-backward splitting algorithm, Mann algorithm and viscosity method. We establish weak and strong convergence theorems for iterative sequences generated by these methods. Our results extend and improve some related results in the literature.