Convergence analysis for fixed point problem of asymptotically nonexpansive mappings and variational inequality problem in Hilbert spaces. (3rd June 2021)

• Record Type: Journal Article
• Authors: Dong, Qiao-Li; Cai, Gang
• Is Part Of: Optimization. Volume 70:Number 5/6(2021)
• Page Start: 1171
• Page End: 1193
• Publication Date: 2021-06-03
• Subjects: Strong convergence -- variational inequality -- fixed point -- asymptotically nonexpansive mapping -- Hilbert spaces; 47H09 -- 47H10; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2020.1789127
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : The purpose of this paper is to study a new viscosity iterative algorithm for finding a common element of the set of fixed points of an asymptotically nonexpansive mapping and the set of solutions of a new variational inequality problem involving inverse-strongly monotone operators in Hilbert spaces. We prove some strong convergence theorems under some suitable assumptions imposed on the parameters by using a modified extragradient method. The results obtained in this paper may be an improvement of many recent ones in this fields.