  In this paper, we investigate a new extragradient algorithm for solving
pseudomonotone equilibrium problems on Hadamard manifolds. The algorithm uses a
variable stepsize which is updated at each iteration and based on some previous
iterates. The convergence analysis of the proposed algorithm is discussed under
mild assumptions. In the case where the equilibrium bifunction is strongly
pseudomonotone, the $R$-linear rate of convergence of the new algorithm is
formulated. A fundamental experiment is provided to illustrate the numerical
behavior of the algorithm. The results presented in this paper generalize some
corresponding known results.
