An Approximation Algorithm for the Combination of G -Variational Inequalities and Fixed Point Problems

Araya Kheawborisut and Atid Kangtunyakarn ()
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Araya Kheawborisut: Department of Mathematics, School of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok 10520, Thailand
Atid Kangtunyakarn: Department of Mathematics, School of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok 10520, Thailand

Mathematics, 2024, vol. 13, issue 1, 1-30

Abstract: In this paper, we introduce a modified form of the G -variational inequality problem, called the combination of G -variational inequalities problem, within a Hilbert space structured by graphs. Furthermore, we develop an iterative scheme to find a common element between the set of fixed points of a G -nonexpansive mapping and the solution set of the proposed G -variational inequality problem. Under appropriate assumptions, we establish a strong convergence theorem within the framework of a Hilbert space endowed with graphs. Additionally, we present the concept of the G -minimization problem, which diverges from the conventional minimization problem. Applying our main results, we demonstrate a strong convergence theorem for the G -minimization problem. Finally, we provide illustrative examples to validate and support our theoretical findings.

Keywords: the combination of G -variational inequality problems; fixed point problem; G -inverse strongly monotone mapping (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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