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Then we introduce a new iterative algorithm for finding a common element of the set of solutions of the equilibrium problem and the set of fixed points of a quasi-<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mrow><mml:mi>\u03d5<\/mml:mi><\/mml:mrow><\/mml:math>-nonexpansive mapping and prove some strong convergence theorems of the iteration. 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