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In this paper, Petrovi´c’s inequality is generalized for h−convex functions, when h is supermultiplicative function. It is noted that the case for h−convex functions does not lead the particular cases for P −function, Godunova-Levin functions, s−Godunova-Levin functions and s−convex functions due to the conditions imposed on h. To cover the case, when h is submultiplicative, Petrovi´c’s inequality is generalized for h−concave functions.