caa a22 4500 465825265 CHVBK 20180323112147.0 cr unu---uuuuu 170327e19901201xx s 000 0 eng 10.1007/BF02112293 doi (NATIONALLICENCE)springer-10.1007/BF02112293 Matkowski J. Department of Mathematics, Technical University, PL-43-300, Bielsko-Biala, Poland aut A functional inequality characterizing convex functions, conjugacy and a generalization of Hölder's and Minkowski's inequalities [Elektronische Daten] [J. Matkowski] Summary: The main result says that, iff: ℝ+ → ℝ+ satisfies the functional inequalityaf(s) + bf(t) ⩽ f (as + bt) (s,t ⩾ 0) for somea, b such that 0 <a < 1 <a + b, thenf(t) = f(1)t, (t ⩾ 0). A relevant result for the reverse inequality is also discussed. Applying these results we determine the form of all functionsf: ℝ k + → ℝ+ satisying the above inequalities. This leads to a characterization of both concave and convex functions defined on ℝ + k−1 , to a notion of "conjugate functions” and to a general inequality which contains Hölder's and Minkowski's inequalities as very special cases. Birkhäuser Verlag, 1990 Primary 39C05, 26B25, 26A21 nationallicence Secondary 39B20 nationallicence aequationes mathematicae Birkhäuser-Verlag 40/1(1990-12-01), 168-180 0001-9054 40:1<168 1990 40 10 https://doi.org/10.1007/BF02112293 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02112293 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Matkowski J. Department of Mathematics, Technical University, PL-43-300, Bielsko-Biala, Poland aut NATIONALLICENCE 773 0- aequationes mathematicae Birkhäuser-Verlag 40/1(1990-12-01), 168-180 0001-9054 40:1<168 1990 40 10 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer