PERTURBATIONS DE FONCTIONS ADDITIVES

Let a ^ 0, a £ 1 and / : (0, oo(-» R be such that f{x+y) = f(x)+ f(y)+o(max{xa,ya}) as max{s,y} J. 0. We show that f{x) = a(x)+o(xa), where a is an additive function, and we use this resuit in studying a second order generalized derivative for real functions.