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Let a and b be fixed real numbers such that 0 0, and such that lim supt!0+ f(t) 0 must be of the form f(t) = f(1)t, t > 0. This improves an earlier result in (5) where, in particular, f is assumed to be nonnegative. Some generalizations for functions defined on cones in linear spaces are given. We apply these results to give a new characterization of the L p -norm. Introduction. We deal with the functional inequality f(as +bt) af(s) +bf(t); where a;b2 R are xed real numbers such that

Convex-like inequality, homogeneity, subadditivity, and a characterization of $L^p$-norm