A strong convergence theorem under a new shrinking projection method for nonlinear mappings in reflexive Banach spaces

In this paper, using a new shrinking projection method, we study the strong convergence theorem for finding a common point of the set of common fixed points of a finite family of Bregman demigeneralized mappings, common zero points of a finite family of Bregman inverse strongly monotone mappings and...

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Bibliographic Details
Published in:Optimization 2023-11, Vol.72 (11), p.2823-2849
Main Authors: Ali, B., Lawan, M. S., Ugwunnadi, G. C., Khan, A. R., Darvish, V.
Format: Article
Language:English
Subjects:
Banach spaces
Bregman demigeneralized map
Bregman distance
Convergence
fixed point
inverse strongly monotone map
maximal monotone map
shrinking projection method
Theorems
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Summary:In this paper, using a new shrinking projection method, we study the strong convergence theorem for finding a common point of the set of common fixed points of a finite family of Bregman demigeneralized mappings, common zero points of a finite family of Bregman inverse strongly monotone mappings and zero points of maximal monotone mapping in reflexive Banach space. Using this result, we get a new strong convergence theorem in Banach space. Our result extends and improves important recent results presented by many authors.
ISSN:0233-1934
1029-4945
DOI:10.1080/02331934.2022.2076233