Convergence results for a zero of the sum of a finite family of maximal monotone mappings in Banach spaces. (3rd July 2022)

• Record Type: Journal Article
• Authors: Wega, Getahun B.; Zegeye, Habtu; Boikanyo, Oganeditse A.
• Is Part Of: Optimization. Volume 71:Number 7(2022)
• Page Start: 1907
• Page End: 1936
• Publication Date: 2022-07-03
• Subjects: Firmly nonexpansive -- Hilbert spaces -- maximal monotone mapping -- strong convergence -- zero points; 47H05 -- 47H09 -- 47H10 -- 47J25 -- 90C25; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2020.1839070
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: The purpose of this paper is to study the method of approximation for zeros of the sum of a finite family of maximal monotone mappings in the setting of Banach spaces. Under some mild conditions, we establish strong convergence results of the proposed approximation method. The assumptions that one of the mappings is single valued and α -inverse strongly monotone are dispensed with. In addition, we give some applications to the minimization problems. Finally, we provide a numerical example which supports our main result. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear mappings.