Abstract
In this article, we introduce an inertial projection and contraction algorithm by combining inertial type algorithms with the projection and contraction algorithm for solving a variational inequality in a Hilbert space H. In addition, we propose a modified version of our algorithm to find a common element of the set of solutions of a variational inequality and the set of fixed points of a nonexpansive mapping in H. We establish weak convergence theorems for both proposed algorithms. Finally, we give the numerical experiments to show the efficiency and advantage of the inertial projection and contraction algorithm.
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