A generalized Halpern-type forward-backward splitting algorithm for solving variational inclusion problems

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Publication Details

Author list: Dechboon, Premyuda; Adamu, Abubakar; Kumam, Poom;

Publisher: AIMS Press

Publication year: 2023

Volume number: 8

Issue number: 5

Start page: 11037

End page: 11056

Number of pages: 20

ISSN: 2473-6988

eISSN: 2473-6988

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-85149732902&doi=10.3934%2fmath.2023559&partnerID=40&md5=ae114dd68424f074f122d9f2ee88917c

Languages: English-Great Britain (EN-GB)

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Abstract

In this paper, we investigate the problem of finding a zero of sum of two accretive operators in the setting of uniformly convex and q-uniformly smooth real Banach spaces (q > 1). We incorporate the inertial and relaxation parameters in a Halpern-type forward-backward splitting algorithm to accelerate the convergence of its sequence to a zero of sum of two accretive operators. Furthermore, we prove strong convergence of the sequence generated by our proposed iterative algorithm. Finally, we provide a numerical example in the setting of the classical Banach space l4(R) to study the effect of the relaxation and inertial parameters in our proposed algorithm. © 2023 the Author(s), licensee AIMS Press.

Keywords

generalized duality mapping, relaxation parameter