<p>The split variational inclusion problem has recently attracted great research attention due to its wide areas of applications. Several iterative methods have been proposed and studied by many researchers for approximating the solution of the problem. However, most of these methods require computation of the operator norm, which is often very difficult to compute or even estimate. In this paper, we introduce a new inertial iterative method (which does not require knowledge of the operator norm) for approximating the common solution of Split Variational Inclusion Problem (SVIP), Equilibrium Problem (EP) and Common Fixed Point Problem (CFPP) of multivalued demicontractive mappings in real Hilbert spaces. Our method employs self-adaptive step size and inertial technique to accelerate the rate of convergence. Under some mild assumptions, we establish the strong convergence of the sequence generated by the proposed algorithm. Finally, we present some applications and numerical examples to illustrate the applicability of our method as well as comparing it with some related methods in the literature. Our results extend and improve some of the existing results in the current literature.</p>