Characterization of convex functions

• Autorzy: Jacek Tabor , Józef Tabor
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 26B25: Convexity, generalizations
• 39B62: Functional inequalities, including subadditivity, convexity, etc.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2009
• Tom: 192
• Numer: 1
• Strony: 29-37

Daty

wydano

2009

Twórcy

autor

Jacek Tabor

• Institute of Mathematics, Jagiellonian University, Łojasiewicza 6, 30-348 Kraków, Poland

autor

Józef Tabor

• Institute of Mathematics, University of Rzeszów, Rejtana 16A, 35-310 Rzeszów, Poland

Identyfikatory

DOI

10.4064/sm192-1-3