A strongly convergent Mann-type inertial algorithm for solving split variational inclusion problems

Abstract

In this paper, we propose a new iterative method for finding an element of the solution set of a split variational inclusion problem in real Hilbert spaces. The iterative scheme is based on a well-known Mann-type method to obtain strong convergence and an inertial method to speed up the convergence rate. We also apply the proposed algorithm to studying the split feasibility problem. Finally, we give some numerical results which show that our proposed algorithm is efficient and implementable from the numerical point of view.