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

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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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Authors and Affiliations

  1. Institute of Mathematics, University of Debrecen, Pf. 12, Debrecen, 4010, Hungary

    Zsolt Páles & Éva Székelyné Radácsi

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  1. Zsolt Páles
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  2. Éva Székelyné Radácsi
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Correspondence to Zsolt Páles.

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Dedicated to the 70th birthdays of Professor Roman Ger and Professor Zygfryd Kominek.

The research of Z. Páles has been supported by the Hungarian Scientific Research Fund (OTKA) Grant K111651. The research of É. S. Radácsi has been supported by the SROP-4.2.2.B-15/1/KONV-2015-0001 project. The project has been supported by the European Union, co-financed by the European Social Fund.

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Páles, Z., Radácsi, É. Characterizations of higher-order convexity properties with respect to Chebyshev systems. Aequat. Math. 90, 193–210 (2016). https://doi.org/10.1007/s00010-015-0377-8

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  • DOI: https://doi.org/10.1007/s00010-015-0377-8

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