Harmonic mappings in the exterior of the unit disk

• Autorzy: Magdalena Gregorczyk , Jarosław Widomski
• Języki publikacji: EN

Abstrakty

EN

In this paper we consider a class of univalent orientation-preserving harmonic functions defined on the exterior of the unit disk which satisfy the condition\(\sum_{n=1}^{\infty}n^{p}(|a_{n}|+|b_{n}|)\leq 1\). We are interested in finding radius of univalence and convexity for such class and we find extremal functions. Convolution, convex combination, and explicit quasiconformal extension for this class are also determined.

Słowa kluczowe

EN

Harmonic mapping; meromorphic; quasiconformal extension; radius of convexity; radius of univalence

• Wydawca: Wydawnictwo Uniwersytetu Marii Curie-Skłodowskiej
• Czasopismo: Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica
• Rocznik: 2010
• Tom: 64
• Numer: 1

Daty

wydano

2010

online

2016-07-29

Twórcy

autor

Magdalena Gregorczyk

autor

Jarosław Widomski

Bibliografia

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• Jahangiri, Jay M., Silverman H., Meromorphic univalent harmonic functions with
• negative coefficients, Bull. Korean Math. Soc. 36 (1999), No. 4, 763-770.
• Lehto O., Virtanen K. I., Quasiconformal Mappings in the Plane, Springer-Verlag, Berlin-Heidelberg-New York, Second Edition, 1973.
• Pommerenke Ch., Univalent Functions, Vandenhoeck & Ruprecht in Gottingen, 1975.
• Sheil-Small T., Complex Polynomials, Cambridge University Press, 2002.

Identyfikatory

DOI

10.17951/a.2010.54.1.63-73