Convergence results for a zero of the sum of a finite family of maximal monotone mappings in Banach spaces

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 o...

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Bibliographic Details
Published in:Optimization 2022-07, Vol.71 (7), p.1907-1936
Main Authors: Wega, Getahun B., Zegeye, Habtu, Boikanyo, Oganeditse A.
Format: Article
Language:English
Subjects:
Approximation
Banach spaces
Convergence
Firmly nonexpansive
Hilbert spaces
Mathematical analysis
maximal monotone mapping
strong convergence
zero points
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Summary: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.
ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2020.1839070