Solution Approximation of Equilibrium Fixed Point Problem and Applications

Abstract

In this work, we prove the strong convergence of an inertial iterative scheme to approximate solutions of the equilibrium fixed point problem associated with nonexpansive mappings in Hilbert spaces. Numerical simulations are carried out to examine the performance of the proposed approach. The results indicate that the proposed inertial approach achieves faster convergence when compared with existing comparable iterative schemes. We also investigate how different choices of initial values influence the convergence behavior of our algorithms and we compare these effects with those observed in classical iterative schemes through graphical illustrations. In applications, we used our approach to solve the signal processing problem. We also apply it to a mathematical model describing the spread of an infectious disease, which illustrates its relevance to real-world dynamical systems. Finally, we show that the proposed method can be applied in solving constrained optimization, variational inequality and split feasibility problems which highlight its flexibility and wide applicability.