G-Tseng’s extragradient method for approximating G-variational inequality problem in Hilbert space endowed with graph

Abstract

In this article, we introduce the $G$-Tseng’s extragradient method, inspired by the extragradient method defined by Korpelevich, for solving $G$-variational inequality problems in Hilbert space. We also address a fixed point problem in a Hilbert space endowed with a graph using the proposed $G$-Tseng’s extragradient method. In the context of Hilbert space, we establish weak and strong convergence theorems for the algorithm. Additionally, we provide numerical examples to support our findings.