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Research Article | Open Access

Two-step inertial method for solving split common null point problem with multiple output sets in Hilbert spaces

Chibueze C. Okeke1, Abubakar Adamu2,3, Ratthaprom Promkam4, Pongsakorn Sunthrayuth4( )
School of Mathematics, University of the Witwatersrand, Johannesburg, South Africa
Operational Research Center in Healthcare, Near East University, Nicosia, TRNC
Mathematics Institute, African University of Science and Technology, Abuja, Nigeria
Department of Mathematics and Computer Science, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi (RMUTT), Pathumthani, Thailand
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Abstract

In this paper, an algorithm with two-step inertial extrapolation and self-adaptive step sizes is proposed to solve the split common null point problem with multiple output sets in Hilbert spaces. Weak convergence analysis are obtained under some easy to verify conditions on the iterative parameters in Hilbert spaces. Preliminary numerical tests are performed to support the theoretical analysis of our proposed algorithm.

Keywords

Hilbert spacemetric projectionself-adaptive step sizetwo-step inertialsplit common null point problem
CLC number: 47H09, 47H10, 49J53, 90C25

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AIMS Mathematics
Volume 8 Issue 9,
September 2023
Pages 20201-20222
DOI: 10.3934/math.20231030

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Cite this article:
Okeke CC, Adamu A, Promkam R, et al. Two-step inertial method for solving split common null point problem with multiple output sets in Hilbert spaces. AIMS Mathematics, 2023, 8(9): 20201-20222. https://doi.org/10.3934/math.20231030

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Received: 21 May 2023
Accepted: 12 June 2023
Published: 15 September 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)