Approximation method for monotone inclusion problems in real Banach spaces with applications

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Author listAbubakar Adamu, Duangkamon Kitkuan, Poom Kumam, Anantachai Padcharoen & Thidaporn Seangwattana

PublisherSpringerOpen

Publication year2022

JournalJournal of Inequalities and Applications (1025-5834)

Volume number2022

Issue number1

ISSN1025-5834

eISSN1029-242X

URLhttps://journalofinequalitiesandapplications.springeropen.com/articles/10.1186/s13660-022-02805-0


Abstract

In this paper, we introduce an inertial Halpern-type iterative algorithm for approximating a zero of the sum of two monotone operators in the setting of real Banach spaces that are 2-uniformly convex and uniformly smooth. Strong convergence of the sequence generated by our proposed algorithm is established by means of some new geometric inequalities proved in this paper that are of independent interest. Furthermore, numerical simulations in image restoration and compressed sensing problems are also presented. Finally, the performance of the proposed method is compared with that of some existing methods in the literature.


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Last updated on 2022-02-09 at 23:05