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Generalized monotonicity in terms of differential inequalities

Part of: Real functions General theory in ordinary differential equations

Published online by Cambridge University Press:  16 January 2019

Mihály Bessenyei
Mihály Bessenyei*
Affiliation:
Institute of Mathematics, University of Debrecen, H-4002 Debrecen, Pf. 400, Hungary (besse@science.unideb.hu)
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Abstract

The classical notions of monotonicity and convexity can be characterized via the nonnegativity of the first and the second derivative, respectively. These notions can be extended applying Chebyshev systems. The aim of this note is to characterize generalized monotonicity in terms of differential inequalities, yielding analogous results to the classical derivative tests. Applications in the fields of convexity and differential inequalities are also discussed.

Keywords

Chebyshev systemgeneralized monotonicitymean value theoremdifferential inequality

MSC classification

Primary: 34A40: Differential inequalities 26A51: Convexity, generalizations 39B62: Functional inequalities, including subadditivity, convexity, etc.
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 149 , Issue 6 , December 2019 , pp. 1473 - 1479
Copyright
Copyright © Royal Society of Edinburgh 2019 

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Footnotes

Dedicated to the 80th birthday of professor Zoltán Daróczy

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