Inertial Extragradient Method for Solving Variational Inequality and Fixed Point Problems of a Bregman Demigeneralized Mapping in a Reflexive Banach Spaces. (11th June 2022)

• Record Type: Journal Article
• Authors: Abass, H. A.; Godwin, G. C.; Narain, O. K.; Darvish, V.
• Is Part Of: Numerical functional analysis and optimization. Volume 43:Number 8(2022)
• Page Start: 933
• Page End: 960
• Publication Date: 2022-06-11
• Subjects: Bregman demigeneralized mapping -- fixed point problem -- iterative scheme -- pseudo-monotone operator -- variational inequality problem; 47H06 -- 47H09 -- 47J05 -- 47J25; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2022.2069813
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: In this paper, by employing a Bregman distance approach, we introduce a self-adaptive inertial extragradient method for finding a common solution of variational inequality problem involving a pseudo-monotone operator and fixed point problem of a Bregman demigeneralized mapping in a reflexive Banach spaces. Using a Bregman distance approach, we establish a strong convergence result for approximating the common solution of the aforementioned problems under some mild assumptions. We display some numerical examples to show the performance of our iterative method. The result presented in this paper extends and complements many related results in literature.