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Sibirsk. Mat. Zh., 2012, Volume 53, Number 3, Pages 597–612 (Mi smj2348)  

Some properties of functions with nonzero order $n$ divided difference

E. G. Kir'yatskiĭ

Vilnius Gediminas Technical University, Vilnius, Lithuania

Abstract: We consider the properties of functions of class $K_n(D)$. This class consists of analytic functions $F(z)$ in a domain $D$ whose nth divided difference does not vanish in $D$. We study some relation of functions of class $K_n(D)$ to Chebyshev systems, consider a few properties of an operator related to a fractional linear transformation of the unit disk, and estimate Taylor series coefficients.

Keywords: analytic function, univalent function, divided difference, function classes, operator, coefficients.

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English version:
Siberian Mathematical Journal, 2012, 53:3, 477–489

Bibliographic databases:

UDC: 517.54
Received: 13.04.2011
Revised: 17.12.2011

Citation: E. G. Kir'yatskiǐ, “Some properties of functions with nonzero order $n$ divided difference”, Sibirsk. Mat. Zh., 53:3 (2012), 597–612; Siberian Math. J., 53:3 (2012), 477–489

Citation in format AMSBIB
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\pages 597--612
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  • Сибирский математический журнал Siberian Mathematical Journal
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