A new inclusion for Bavrin's families of holomorphic functions in n-circular domains

The paper concerns inclusions of Bavrin families of complex valued functions which are hololomorphic in bounded complete -circular domains and fulfil some geometric conditions. Such families were applied later to research some families of locally biholomorphic mappings in . (see for instance, J. A....

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Bibliographic Details
Published in:Mathematica Slovaca Vol. 66; no. 4; pp. 845 - 852
Main Authors: Długosz, Renata, Leś, Edyta, Sibelska, Agnieszka
Format: Journal Article
Language:English
Published: Heidelberg De Gruyter 01.08.2016
Walter de Gruyter GmbH
Subjects:
30C45
Circularity
Complex variables
Extreme values
Functions (mathematics)
holomorphic functions of several complex variables
Inclusions
Mapping
Mathematical analysis
n-circular domains
Primary 32A30
starlike and convex functions
the Minkowski function
the Temljakov operator
Theorems
ISSN:0139-9918, 1337-2211
Online Access:Get full text
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Summary:The paper concerns inclusions of Bavrin families of complex valued functions which are hololomorphic in bounded complete -circular domains and fulfil some geometric conditions. Such families were applied later to research some families of locally biholomorphic mappings in . (see for instance, J. A. Pfaltzgraff and T. J Suffridge, P. Liczberski, I. Graham and G. Kohr, H. Hamada, T. Honda, G. Kohr). Some results for functions of such families were obtained by [BAVRIN, I. I.: , Moskov Obl. Ped. Inst., Moscow, 1976 (Russian)], [DŁUGOSZ, R.: , J. Appl. Anal. (2013), 153--165], [DŁ UGOSZ, R.—LEŚ, E.: , Complex Var. Elliptic Equ. (2014), 883--899], [LEŚ-BOMBA, E.—LICZBERSKI, P.: , Demonstratio Math. (2009), 491--503], et al..
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ISSN:0139-9918
1337-2211
DOI:10.1515/ms-2015-0187