A new multi-step iterative algorithm for approximating common fixed points of a finite family of multi-valued bregman relatively nonexpansive mappings
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Author list: Kumam W., Sunthrayuth P., Phunchongharn P., Akkarajitsakul K., Ngiamsunthorn P.S., Kumam P.
Publisher: MDPI
Publication year: 2016
Journal: Algorithms (1999-4893)
Volume number: 9
Issue number: 2
ISSN: 1999-4893
eISSN: 1999-4893
Languages: English-Great Britain (EN-GB)
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Abstract
In this article, we introduce a new multi-step iteration for approximating a common fixed point of a finite class of multi-valued Bregman relatively nonexpansive mappings in the setting of reflexive Banach spaces. We prove a strong convergence theorem for the proposed iterative algorithm under certain hypotheses. Additionally, we also use our results for the solution of variational inequality problems and to find the zero points of maximal monotone operators. The theorems furnished in this work are new and well-established and generalize many well-known recent research works in this field. ฉ 2016 by the authors.
Keywords
Iterative methods, Maximal monotone, Multi-valued Bregman relatively nonexpansive mapping, Reflexive Banach spaces
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