Iterative algorithm for solving monotone inclusion and fixed point problem of a finite family of demimetric mappings

The goal of this study is to develop a novel iterative algorithm for approximating the solutions of the monotone inclusion problem and fixed point problem of a finite family of demimetric mappings in the context of a real Hilbert space. The proposed algorithm is based on the inertial extrapolation step strategy and combines forward-backward and Tseng's methods. We introduce a demimetric operator with respect to $M$-norm, where $M$ is a linear, self-adjoint, positive and bounded operator. The algorithm also includes a new step for solving the fixed point problem of demimetric operators with respect to the $M$-norm. We study the strong convergence behavior of our algorithm. Furthermore, we demonstrate the numerical efficiency of our algorithm with the help of an example. The result given in this paper extends and generalizes various existing results in the literature.