Mann-type algorithms for variational inequality problems and fixed point problems. (2nd October 2020)

• Record Type: Journal Article
• Authors: Viet Thong, Duong; Van Hieu, Dang
• Is Part Of: Optimization. Volume 69:Number 10(2020)
• Page Start: 2305
• Page End: 2326
• Publication Date: 2020-10-02
• Subjects: Subgradient extragradient method -- Mann-type method -- inertial method -- Tseng's extragradient method -- variational inequality problem -- fixed point problem; 65Y05 -- 65K15 -- 68W10 -- 47H05 -- 47H10; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2019.1692207
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : The purpose of this paper is to investigate the problem of finding a common element of the solution set of a variational inequality problem for a monotone, Lipschitz-continuous mapping and set of fixed point of a quasi-nonexpansive mapping. We introduce Mann-type Tseng's extragradient-like approximation method which is based on so-called inertial Tseng's extragradient method and Mann method. We establish two weak convergence theorems for two iterative sequences generated by these methods. Our results extend and improve some related results in the literatures.