Inertial algorithm for solving equilibrium, variational inclusion and fixed point problems for an infinite family of strict pseudocontractive mappings

In this paper, we study the problem of finding common solutions of equilibrium problems, variational inclusion problems and fixed point problems for an infinite family of strict pseudocontractive mappings. We propose an iterative algorithm, which combines inertial methods with viscosity methods, for approximating common solutions of the above problems. Under mild conditions, we prove a strong theorem in Hilbert spaces and apply our result to optimization problems. Finally, we present a numerical example to demonstrate the efficiency of our algorithm in comparison with other existing methods in the literature.