A novel algorithm for approximating common solution of a system of monotone inclusion problems and common fixed point problem

<p style='text-indent:20px;'>In this paper, we study the problem of finding a common element set solutions system monotone inclusion problems and fixed points finite family generalized demimetric mappings in Hilbert spaces. We propose new efficient algorithm for solving problem. Our method relies on inertial algorithm, Tseng's splitting viscosity algorithm. Strong convergence analysis proposed is established under standard mild conditions. As applications use our to variational inequality problems, constrained multiple-set split convex feasibility problem, minimization minimizer Finally, give some numerical results show that implementable from point view.</p>