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In this paper, we introduce a new hybrid algorithm for solving equilibriumproblems. The algorithm combines the extragradient method and the hybrid (outerapproximation) method. In this algorithm, only an optimization program issolved at each iteration without the extra-steps like as in the extragradientmethod and the Armijo linesearch method. A specially constructed half-space inthe hybrid method is the reason for the absence of an optimization program inour algorithm. The strong convergence theorem is established and severalnumerical experiments are implemented to illustrate the convergence of thealgorithm and compare it with others.

An extension of hybrid method without extrapolation step to equilibrium problems