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Characterization of higher-order monotonicity via integral inequalities

Published online by Cambridge University Press:  04 August 2010

Mihály Bessenyei  and
Zsolt Páles
Zsolt Páles
Affiliation:
Institute of Mathematics, University of Debrecen, 4010 Debrecen, Pf. 12, Hungary ([email protected]; [email protected])
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Abstract

The Hermite-Hadamard inequality not only is a consequence of convexity but also characterizes it: if a continuous function satisfies either its left-hand side or its right-hand side on each compact subinterval of the domain, then it is necessarily convex. The aim of this paper is to prove analogous statements for the higher-order extensions of the Hermite-Hadamard inequality. The main tools of the proofs are smoothing by convolution and the support properties of higher-order monotone functions.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 140 , Issue 4 , August 2010 , pp. 723 - 736
Copyright
Copyright © Royal Society of Edinburgh 2010

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