Strong convergence of a self-adaptive inertial Tseng's extragradient method for pseudomonotone variational inequalities and fixed point problems

Abstract In this paper, we study the problem of finding a common solution pseudomonotone variational inequality and fixed point for demicontractive mappings. We introduce new inertial iterative scheme that combines Tseng’s extragradient method with viscosity together adaptive step size technique investigated problem. prove strong convergence result our proposed algorithm under mild conditions without prior knowledge Lipschitz constant operator in Hilbert spaces. Finally, present some numerical experiments to show efficiency comparison existing methods literature.