New inertial viscosity Tseng’s extragradient method with self-adaptive step size in nding Common solution to variational inequality problem

Abstract

In this article, we study and propose new inertial viscosity Tseng’s extragradient algorithm with self-adaptive step size in nding common solution to Variational Inequality Problem or VIP for short in Hilbert space. Our proposed method involves a projection onto a halfspace and using selfadaptive step size for approximating the minimum-norm of the VIP. Then, we apply our results
in nding a common solution of VIP for an innite family of monotone and Lipschitz continuous operators. Furthermore, our results extend and generalize some existing results in the literature.