In this paper, a new algorithm is considered to find a common element of
the solution set of a pseudomonotone equilibrium problem and the fixed
point set for a quasi-nonexpansive mapping in a real Hilbert space. The
algorithm is based on the subgradient extragradient method, the inertial
method and the viscosity method. The adaptive step size ensures that the
algorithm does not need to know apriori the Lipschitz constants of the
associated bifunction. Under standard assumptions, the strong
convergence of the proposed algorithm was studied . Moreover, numerical
experiments on several specific problems and comparison with other
algorithms show the superiority of the algorithm.