An algorithm for solving the variational inequality problem over the solution set of the split variational inequality and fixed point problem

Abstract

In this paper, we introduce a new algorithm for solving strongly monotone variational inequality problem, where the constraint set is the solution set of the split variational inequality and fixed point problem. Our method uses dynamic step sizes selected based on information of the previous step, which gives strong convergence result without the prior knowledge of the given bounded linear operator’s norm. In addition, using our method, we do not require any information of the Lipschitz and strongly monotone constants of the mappings. Several corollaries of our main result are also presented. Finally, a numerical example has been given to illustrate the effectiveness of our proposed algorithm.