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differential inequality

Proceedings of the Royal Society of Edinburgh Section A: Mathematics (1)

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1 results

Generalized monotonicity in terms of differential inequalities
Part of
- Real functions
- General theory in ordinary differential equations
Mihály Bessenyei
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 149 / Issue 6 / December 2019

Published online by Cambridge University Press:

16 January 2019, pp. 1473-1479

Print publication:

December 2019
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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.