Distortion theorems in the class Kn(D)

• Autorzy: Kir'yatskii E. G.
• Języki publikacji: EN

Abstrakty

EN

This article presents the analysis of properties of functions belonging to the class Kn(D) earlier introduced by the author. This is a class of functions analytical in the domain D, for which the n-th divided difference [F; zo, . . . , zn] [...]consisting of functions univalent in the domain D is obtained. The subclass Kn(E), formed by functions F(z) = zn + an+izn+1 + .... analytical in a unit circle E is separated from class Kn(D) and its properties are considered. The author touches classical and at the same time urgent questions, arising at the study of analytical functions, belonging to some class.

Słowa kluczowe

EN

analytical functions; distortion theorems

PL

funkcje analityczne; teoria zniekształceń

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2008
• Tom: Vol. 41, nr 3
• Strony: 543--549
• Opis fizyczny: Bibliogr. 4 poz.

Twórcy

autor

Kir'yatskii E. G.

• Vilnius Gediminas Technical University, Vilnius, Lietuva,

Bibliografia

• [1] I. I. Ibragimov, Methods of Interpolation and Some Applications, Moskva, Nauka, 1971, 519 p. (in Russian).
• [2] E. G. Kiriyatzkii, On functions with nonwanishing n-th divided difference, Lith. Math. J. I 1-2 (1961), 109-114 (in Russian).
• [3] I. A. Aleksandrov, Methods of geometrical theory of analytical functions, Tomsk University, 2001, 220 p. (in Russian).
• [4] P. Koebe, Uber die Uniformisirung der algebraishen Kurven durch automorphe Funktionen mit imaginarer Substitutionsgruppe, Nachr. Rgl. Qes. Wiss Qottingen, Math.-Phys. Kl., 1909, 68-76.