Splitting method involving two-step inertial for solving inclusion and fixed point problems with applications

In this article, two-step inertial method is proposed for finding zero point of the sum of two monotone operators and fixed-point of κ-strictly pseudo-nonspreading mapping in a real Hilbert space. Weak convergence of the sequence of the proposed method is obtained under less restrictive conditions. With suitable numerical examples, the method is shown to be robust in terms of speed of convergence. It is also shown to be an improvement over one-step inertial method, which has been used by many authors in the literature to solve similar problems.