  In this paper, we propose new algorithms for finding a common point of the
solution set of a pseudomonotone equilibrium problem and the set of fixed
points of a symmetric generalized hybrid mapping in a real Hilbert space. The
convergence of the iterates generated by each method is obtained under
assumptions that the fixed point mapping is quasi-nonexpansive and demiclosed
at $0$, and the bifunction associated with the equilibrium problem is weakly
continuous. The bifunction is assumed to be satisfying a Lipschitz-type
condition when the basic iteration comes from the extragradient method. It
becomes unnecessary when an Armijo back tracking linesearch is incorporated in
the extragradient method.
