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An Approximation Algorithm for the Combination of G-Variational Inequalities and Fixed Point Problems
Author(s)
Kheawborisut, Araya
Date Issued
January 1, 2025
Type
Article
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.
Citation
Mathematics, 13(1), 2025