Displaying similar documents to “Two mappings associated with Jensen's inequality.”

Characterization of convex functions

Jacek Tabor, Józef Tabor (2009)

Studia Mathematica

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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.

General Lebesgue integral inequalities of Jensen and Ostrowski type for differentiable functions whose derivatives in absolute value are h-convex and applications

Sever Dragomir (2015)

Annales Universitatis Mariae Curie-Sklodowska, sectio A – Mathematica

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Some inequalities related to Jensen and Ostrowski inequalities for general Lebesgue integral of differentiable functions whose derivatives in absolute value are h-convex are obtained. Applications for f-divergence measure are provided as well.