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RADII OF HARMONIC MAPPINGS IN THE PLANE

Part of: Two-dimensional theory Geometric function theory

Published online by Cambridge University Press:  08 July 2016

BO-YONG LONG  and
HUA-YING HUANG
BO-YONG LONG*
Affiliation:
School of Mathematical Sciences, Anhui University, Hefei 230601, China email longboyong@ahu.edu.cn
HUA-YING HUANG
Affiliation:
School of Mathematical Sciences, Anhui University, Hefei 230601, China email huanghuaying50@163.com
*
✉longboyong@ahu.edu.cn
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Abstract

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In this paper, for the convolution and convex combination of harmonic mappings, the radii of univalence, full convexity and starlikeness of order $\unicode[STIX]{x1D6FC}$ are explored. All results are sharp. By way of application, the univalent radius and the Bloch constant of the convolution of two bounded harmonic mappings are obtained.

Keywords

harmonic mappingsradiusfully convex of order 𝛼fully starlike of order 𝛼convex combinationconvolutionBloch constant

MSC classification

Primary: 31A05: Harmonic, subharmonic, superharmonic functions
Secondary: 30C45: Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 102 , Issue 3 , June 2017 , pp. 331 - 347
Copyright
© 2016 Australian Mathematical Publishing Association Inc. 

Footnotes

The research was supported by the NSFC (no. 11501002), Doctoral Research Start-up Funds Projects of Anhui University (numbers J10113190002 and 01001901) and partially by China Scholarship Council.

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