Approximation of Solutions of Split Monotone Variational Inclusion Problems and Fixed Point Problems

Abstract

Many researchers have incorporated an inertial term and will continue to involve it in iterative algorithms due to the fact that it speeds up the rate of convergence which is desirable in applications. In this paper, we propose a new inertial extrapolation algorithm for solving split monotone variational inclusion problems which turns out to solve fixed point problems in the framework of real Hilbert spaces. Our proposed algorithm which is the generalization of split feasibility problems among many others, does not involve the knowledge of operator norm which is sometimes difficult in practice. Furthermore, we prove under some mild assumptions that the sequence generated recursively by our algorithm converges strongly to a common solution of split monotone variational inclusion problems and fixed point of κ-demicontractive mapping. Finally, we apply our algorithm to solve other related problems, precisely linear inverse problems. Some numerical illustrations are provided to further demonstrate the efficiency and competitiveness of our algorithm.