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Article . 2001
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Monotonicity of the integral mean and convex functions

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 2001Publisher:Heldermann, Lemgo
Authors: Fischer, P.; Slodkowski, Z.;

Monotonicity of the integral mean and convex functions

Abstract

Summary: A set \(A\) will be said convexly majorized by a set \(B\) if the integral mean of any convex function over \(A\) is not exceeding its mean over \(B\). Sufficient conditions and necessary conditions are presented about this relation. Methods are introduced which generate such sets \(A\) and \(B\).

Keywords

convex function, Inequalities for sums, series and integrals, integral mean, convex majorization, monotonicity, mean-value inequalities, Convexity of real functions of several variables, generalizations

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
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