Viscosity extragradient algorithms with double inertial extrapolation steps for quasimonotone variational inequalities and fixed point problems

Abstract

We study two viscosity extragradient algorithms with double inertial extrapolation steps for finding a common solution of a variational inequality governed by a quasimonotone operator and of a fixed point problem with a demicontractive mapping in a real Hilbert space. The strong convergence theorems are proved under certain appropriate conditions. The step sizes of our algorithms are updated by simple calculations without knowing the prior information of the operator norms. Numerical examples in finite- and infinite-dimensional spaces are given to show the performance of the proposed algorithms.