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Complex Variables and Elliptic Equations
An International Journal
Volume 58, 2013 - Issue 12
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Articles

Solution to an open problem on convolutions of harmonic mappings

Liulan Li Department of Mathematics and Computational Science, Hengyang Normal University, Hengyang, Hunan 421008, People's Republic of China
&
Saminathan Ponnusamy Department of Mathematics, Indian Institute of Technology Madras, Chennai 600 036, IndiaCorrespondence[email protected]
Pages 1647-1653 | Received 01 Mar 2012, Accepted 08 Jun 2012, Published online: 25 Sep 2012
 
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Abstract

The convolution of two univalent harmonic mappings of the unit disc onto convex domains is not necessarily univalent. Dorff, Nowak and Wołoszkiewicz formulated an open problem concerning the convolution of two right half-plane mappings when one of them is fixed. In this article we solve this open problem.

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Acknowledgements

The first author was supported by NSF of Hunan (No. 10JJ4005), Hunan Provincial Education Department (No. 11B019) and the Construct Program of the Key Discipline in Hunan province.

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