Approximation method for monotone inclusion problems in real Banach spaces with applications
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Author list: Abubakar Adamu, Duangkamon Kitkuan, Poom Kumam, Anantachai Padcharoen & Thidaporn Seangwattana
Publisher: SpringerOpen
Publication year: 2022
Journal: Journal of Inequalities and Applications (1025-5834)
Volume number: 2022
Issue number: 1
ISSN: 1025-5834
eISSN: 1029-242X
URL: https://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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