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001-es BibID:	BIBFORM076806
Első szerző:	Páles Zsolt (matematikus)
Cím:	A new characterization of convexity with respect to Chebyshev systems / Zsolt Páles, Éva Székelyné Radácsi
Dátum:	2018
ISSN:	1846-579X 1848-9575
Megjegyzések:	The notion of nth order convexity in the sense of Hopf and Popoviciu is defined via the nonnegativity of the (n + 1)st order divided differences of a given real-valued function. In view of the well-known recursive formula for divided differences, the nonnegativity of (n + 1)st order divided differences is equivalent to the (n - k - 1)st order convexity of the kth order divided differences which provides a characterization of nth order convexity. The aim of this paper is to apply the notion of higher-order divided differences in the context of convexity with respect to Chebyshev systems introduced by Karlin in 1968. Using a determinant identity of Sylvester, we then establish a formula for the generalized divided differences which enables us to obtain a new characterization of convexity with respect to Chebyshev systems. Our result generalizes that of Wasowicz which was obtained in 2006. As an application, we derive a necessary condition for functions which can be written as the difference of two functions convex with respect to a given Chebyshev system.
Tárgyszavak:	Természettudományok Matematika- és számítástudományok idegen nyelvű folyóiratközlemény külföldi lapban
Megjelenés:	Journal of Mathematical Inequalities. - 12 : 3 (2018), p. 605-617. -
További szerzők:	Székelyné Radácsi Éva (1990-) (matematikus)
Pályázati támogatás:	OTKA K-111651 OTKA EFOP-3.6.1-16-2016-00022 EFOP
Internet cím:	Szerző által megadott URL DOI Intézményi repozitóriumban (DEA) tárolt változat
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