Characterization of convex functions

Tom 192 / 2009

Jacek Tabor, Józef Tabor Studia Mathematica 192 (2009), 29-37 MSC: 26B25, 39B62. DOI: 10.4064/sm192-1-3

Streszczenie

There are many inequalities which in the class of continuous functions are equivalent to convexity (for example the Jensen inequality and the Hermite–Hadamard inequalities). We show that this is not a coincidence: every nontrivial linear inequality which is valid for all convex functions is valid only for convex functions.

Autorzy

  • Jacek TaborInstitute of Mathematics
    Jagiellonian University
    /Lojasiewicza 6
    30-348 Krak/ow, Poland
    e-mail
  • Józef TaborInstitute of Mathematics
    University of Rzesz/ow
    Rejtana 16A
    35-310 Rzesz/ow, Poland
    e-mail

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