Displaying similar documents to “On minimizing noncoercive functionals on weakly vlosed sets”

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

Janusz Matkowski, Marek Pycia (1995)

Annales Polonici Mathematici

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Let a and b be fixed real numbers such that 0 < mina,b < 1 < a + b. We prove that every function f:(0,∞) → ℝ satisfying f(as + bt) ≤ af(s) + bf(t), s,t > 0, and such that l i m s u p t 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.