A modified iterative Method for Solving Split variational Inclusion Problems and Fixed Point Problems for Nonexpansive Semigroup

Abstract In this paper, we introduce and study a modified iterative method for approximating a common solution of split variational inclusion problems and fixed point problems for nonexpansive semigroup in real Hilbert spaces. We prove that the proposed method converges strongly to the solution of the mentioned problem under some mild assuptions. A new inertial extrapolation is introduced which is known to speed up the rate of covergence of iterative algorithms. Our method uses self-adaptive stepsize that is generated at each iteration. It does not depend on the operator norm which is difficult in practice. We give numerical illustrations of the proposed scheme in comparison with others in the literature to further justify the applicability and efficiency of our proposed algorithm. AMS Subject Classification: 47H09, 47J25.