A common solution of f-fixed point and variational inequality problems in Banach spaces. (4th March 2023)

• Record Type: Journal Article
• Authors: Zegeye, Habtu; Boikanyo, Oganeditse A.
• Is Part Of: Optimization. Volume 72:Number 3(2023)
• Page Start: 737
• Page End: 762
• Publication Date: 2023-03-04
• Subjects: f-fixed point -- f-pseudocontractive mapping -- monotone mapping -- semi-pseudocontractive mapping -- variational inequality; 47H09 -- 47H10 -- 47J25 -- 47J05 -- 47J20; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2021.1982939
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: In this paper, we construct a Halpern-type subgradient extragradient iterative algorithm which converges strongly to a common point of the f -fixed point set of a continuous f -pseudocontractive mapping and the solutions set of a variational inequality problem for Lipschitz monotone mapping in reflexive real Banach spaces. In addition, a numerical example is given to demonstrate the behaviour of the convergence of the algorithm. Our results improve, generalize and unify some related recent results in the literature.