Inertial extragradient algorithms with non-monotonic step sizes for solving variational inequalities and fixed point problems

摘要

In this paper, we introduce four inertial extragradient algorithms with non-monotonic step sizes to find the solution of the convex feasibility problem, which consists of a monotone variational inequality problem and a fixed point problem with a demicontractive mapping. Strong convergence theorems of the suggested algorithms are established under some standard conditions. Finally, we implement some computational tests to show the efficiency and advantages of the proposed algorithms and compare them with some existing ones.