Characterizations of higher-order convexity properties with respect to Chebyshev systems
Classical Analysis and ODEs
2017-06-29 v1
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.
Keywords
Cite
@article{arxiv.1505.00617,
title = {Characterizations of higher-order convexity properties with respect to Chebyshev systems},
author = {Zsolt Páles and Éva Székelyné Radácsi},
journal= {arXiv preprint arXiv:1505.00617},
year = {2017}
}