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Sufficient conditions are obtained in order to guarantee Hyers\u2010Ulam\u2010Rassias, <jats:italic>\u03c3<\/jats:italic>\u2010semi\u2010Hyers\u2010Ulam and Hyers\u2010Ulam stabilities for those integral equations. Finite and infinite intervals are considered as integration domains. Those sufficient conditions are obtained based on the use of fixed point arguments within the framework of the Bielecki metric and its generalizations. 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