Displaying similar documents to “Remarks on “On a converse of Jensen's discrete inequality” of S. Simić.”

Generalizations of Jensen-Steffensen and related integral inequalities for superquadratic functions

Shoshana Abramovich, Slavica Ivelić, Josip Pečarić (2010)

Open Mathematics

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We present integral versions of some recently proved results which improve the Jensen-Steffensen and related inequalities for superquadratic functions. For superquadratic functions which are not convex we get inequalities analogous to the integral Jensen-Steffensen inequality for convex functions. Therefore, we get refinements of all the results which use only the convexity of these functions. One of the inequalities that we obtain for a superquadratic function φ is y ¯ ⩾ φ x ¯ + 1 λ β - λ α ∫ α β φ f t - x ¯ d λ t , where x ¯ = 1 λ β - λ α ∫ α β f t d λ t and y ¯ = 1 λ β - λ α ∫ α β φ f t d λ t which...

Generalizations of the Jensen-Steffensen and related inequalities

Milica Bakula, Marko Matić, Josip Pečarić (2009)

Open Mathematics

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We present a couple of general inequalities related to the Jensen-Steffensen inequality in its discrete and integral form. The Jensen-Steffensen inequality, Slater’s inequality and a generalization of the counterpart to the Jensen-Steffensen inequality are deduced as special cases from these general inequalities.

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.