1Institute of Mathematics Jagiellonian University /Lojasiewicza 6 30-348 Krak/ow, Poland 2Institute of Mathematics University of Rzesz/ow Rejtana 16A 35-310 Rzesz/ow, Poland
Studia Mathematica, Tome 192 (2009) no. 1, pp. 29-37
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.
Keywords:
there many inequalities which class continuous functions equivalent convexity example jensen inequality hermite hadamard inequalities coincidence every nontrivial linear inequality which valid convex functions valid only convex functions
Affiliations des auteurs :
Jacek Tabor
1
;
Józef Tabor
2
1
Institute of Mathematics Jagiellonian University /Lojasiewicza 6 30-348 Krak/ow, Poland
2
Institute of Mathematics University of Rzesz/ow Rejtana 16A 35-310 Rzesz/ow, Poland
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Jacek Tabor; Józef Tabor. Characterization of convex functions. Studia Mathematica, Tome 192 (2009) no. 1, pp. 29-37. doi: 10.4064/sm192-1-3
