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Numerical Functional Analysis and Optimization Volume 42, 2021 - Issue 14: Fixed Points Theory and Nonlinear Functional Analysis, Part 2
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Articles

Splitting Algorithms for Equilibrium Problems and Inclusion Problems on Hadamard Manifolds

Konrawut Khammahawonga Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), Bangkok, Thailand;b Fixed Point Research Laboratory, Fixed Point Theory and Applications Research Group, Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), Bangkok, ThailandORCID Iconhttps://orcid.org/0000-0002-7423-8519View further author information
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Poom Kumamb Fixed Point Research Laboratory, Fixed Point Theory and Applications Research Group, Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), Bangkok, Thailand;c Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), Bangkok, ThailandORCID Iconhttps://orcid.org/0000-0002-5463-4581View further author information
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Parin Chaipunyaa Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), Bangkok, Thailand;d NCAO Research Center, Fixed Point Theory and Applications Research Group, Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), Bangkok, ThailandCorrespondence[email protected]
ORCID Iconhttps://orcid.org/0000-0002-0207-6098View further author information
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Pages 1645-1682 | Received 16 Jan 2020, Accepted 13 Nov 2020, Published online: 07 Jul 2021
 
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Abstract

The aim of this article is to introduce new iterative algorithms for finding a common solution from the set of equilibrium points of an equilibrium problem and of singularities of an inclusion problem on Hadamard manifolds. We discuss some particular cases of the problem with the proposed algorithms. The convergence results of a sequence generated by the proposed algorithms are proved under mild assumptions on a Hadamard manifold. Moreover, we apply our results to solve optimization problems and variational inequality problems.

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Funding

The first author was financially supported by the Research Professional Development Project Under the Science Achievement Scholarship of Thailand (SAST), and the last author was supported by KMUTT Research Fund. This project is supported by Center of Excellence in Theoretical and Computational Science (TaCS-CoE), KMUTT. Moreover, this research project is supported by Thailand Science Research and Innovation (TSRI) Basic Research Fund: Fiscal year 2021 under project number 64A306000005.

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