<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si4.svg" display="inline" id="d1e264"> <mml:mi mathvariant="script">G</mml:mi> </mml:math> -Tseng’s extragradient method for approximating <mml:math xmlns:mml="http://www.w3.org/1998/Ma

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.