Abstract
The key idea of this article is to propose two inertial subgradient extragradient methods for solving two classes of equilibrium problems in the setting of real Hilbert space. Weak convergence and strong convergence of the proposed algorithms are established based on certain mild conditions. We also apply our results to obtain the numerical solution of a variational inequality and fixed problems. Numerical findings suggest that the proposed algorithms are more efficient than some existing methods for equilibrium problems.