Double-step inertial algorithms for equilibrium and fixed point problems in Hilbert spaces

Abstract.

In this paper, we introduce a novel double-inertial algorithm for simultaneously solving equilibrium problems and finding common fixed points of countable families of nonexpansive mappings in real Hilbert spaces. Under mild conditions on the inertial parameters and step sizes, we establish a weak convergence theorem for the proposed method. Furthermore, we provide numerical experiments that demonstrate the algorithm’s convergence behavior and compare its performance with existing methods.