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001-es BibID:	BIBFORM126143
035-os BibID:	(WoS)001342491800001
Első szerző:	Kiss Tibor (matematikus)
Cím:	On the [sigma]-balancing property of multivariate generalized quasi-arithmetic means / Kiss Tibor, Nagy Gergő
Dátum:	2024
ISSN:	1331-4343 1848-9966
Megjegyzések:	The aim of this paper is to characterize the so-called sigma-balancing property in the class of generalized quasi-arithmetic means. In general, the question is whether those elements of a given family of means that possess this property are quasi-arithmetic. The first result in the latter direction is due to G. Aumann who showed that a balanced complex mean is necessariliy quasi-arithmetic provided that it is analytic. Then Aumann characterized quasi-arithmetic means among Cauchy means in terms of the balancing property. These results date back to the 1930s. In 2015, Lucio R. Berrone, generalizing balancedness, concluded that a mean having that more general property is quasi-arithmetic if it is symmetric, strict and continuously differentiable. A common feature of these results is that they assume a certain order of differentiability of the mean whether or not it is a natural condition. In 2021, the balancing property was characterized in the family of generalized quasiarithmetic means of two variables under only natural conditions, namely continuity and strict monotonicity of their generating functions. Here we extend the corresponding result for multivariate generalized quasi-arithmetic means by relaxing the conditions on the generating functions and considering the more general sigma-balancing property.
Tárgyszavak:	Természettudományok Matematika- és számítástudományok idegen nyelvű folyóiratközlemény külföldi lapban folyóiratcikk balanced means balancing property Aumann's equation generalized quasiarithmetic mean
Megjelenés:	Mathematical Inequalities & Applications. - 27 : 4 (2024), p. 1009-1019. -
További szerzők:	Nagy Gergő (1983-) (matematikus)
Pályázati támogatás:	K-134191 OTKA
Internet cím:	Szerző által megadott URL DOI Intézményi repozitóriumban (DEA) tárolt változat
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