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arXiv · 1505.00617

Characterizations of higher-order convexity properties with respect to Chebyshev systems

Zsolt Páles·Éva Székelyné Radácsi
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Abstract

In this paper various notions of convexity of real functions with respect to Chebyshev systems defined over arbitrary subsets of the real line are introduced. As an auxiliary notion, a concept of a relevant divided difference and also a related lower Dinghas type derivative are also defined. The main results of the paper offer various characterizations of the convexity notions in terms of the nonnegativity of a generalized divided difference and the corresponding lower Dinghas type derivative.

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Zsolt Páles, Éva Székelyné Radácsi. 2015-05-04. Characterizations of higher-order convexity properties with respect to Chebyshev systems. https://doi.org/10.1007/s00010-015-0377-8

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