Harmonic mappings in the exterior of the unit disk

Magdalena Gregorczyk, Jarosław Widomski

Abstract


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.

Keywords


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

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References


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DOI: http://dx.doi.org/10.2478/v10062-010-0005-y
Date of publication: 2016-07-29 22:06:16
Date of submission: 2016-07-29 21:18:18


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Copyright (c) 2010 Magdalena Gregorczyk, Jarosław Widomski