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


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.


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

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