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

Research output: Contribution to journalArticle

2 Citations (Scopus)

### 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.

Original language English 193-210 18 Aequationes Mathematicae 90 1 https://doi.org/10.1007/s00010-015-0377-8 Published - Feb 1 2016

### Fingerprint

Chebyshev System
Divided Differences
Convexity
Higher Order
Derivatives
Derivative
Nonnegativity
Real Line
Subset
Arbitrary

### Keywords

• Chebyshev system
• Generalized convexity
• Generalized divided difference
• Generalized lower Dinghas type derivative

### ASJC Scopus subject areas

• Mathematics(all)
• Applied Mathematics
• Discrete Mathematics and Combinatorics

### Cite this

Characterizations of higher-order convexity properties with respect to Chebyshev systems. / Páles, Z.; Radácsi, Éva Székelyné.

In: Aequationes Mathematicae, Vol. 90, No. 1, 01.02.2016, p. 193-210.

Research output: Contribution to journalArticle

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