A Relaxed Two-Inertial Subgradient Extragradient Method for Solving Equilibrium and Fixed Point Problems with Applications

In this research, we introduce an improved pseudomonotone subgradient extragradient algorithm for finding common solutions of equilibrium and fixed point problems in real Hilbert spaces. We obtain the strong convergence results of the proposed method under some mild and suitable assumptions on the control parameters. Unlike many existing methods that rely on contraction, and Mann-like techniques to obtain strong convergence, our method employs the typical Mann iteration technique which does requires complex computations. Furthermore, our method incorporates a relaxed two-inertial technique which enhances its speed of convergence. Additionally, we demonstrate the applicability of our findings to variational inequality problems, and image recovery problems. Finally, we present some numerical experiments to validate our theoretical results and show the superiority of our method over some well known results in the literature. The obtained results in this paper improve, extend and unify many existing results in this research direction.