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2014 Coefficient conditions for harmonic univalent mappings and hypergeometric mappings
S.V. Bharanedhar, S. Ponnusamy
Rocky Mountain J. Math. 44(3): 753-777 (2014). DOI: 10.1216/RMJ-2014-44-3-753

Abstract

In this paper, we obtain coefficient criteria for a normalized harmonic function defined in the unit disk to be close-to-convex and fully starlike, respectively. Using these coefficient conditions, we present different classes of harmonic close-to-convex (respectively, fully starlike) functions involving Gaussian hypergeometric functions. In addition, we present a convolution characterization for a class of univalent harmonic functions discussed recently by Mocanu, and later by Bshouty and Lyzzaik in 2010. Our approach provides examples of harmonic polynomials that are close-to-convex and starlike, respectively.

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S.V. Bharanedhar. S. Ponnusamy. "Coefficient conditions for harmonic univalent mappings and hypergeometric mappings." Rocky Mountain J. Math. 44 (3) 753 - 777, 2014. https://doi.org/10.1216/RMJ-2014-44-3-753

Information

Published: 2014
First available in Project Euclid: 28 September 2014

zbMATH: 1298.30001
MathSciNet: MR3264481
Digital Object Identifier: 10.1216/RMJ-2014-44-3-753

Subjects:
Primary: 30C45

Keywords: close-to-convex , Coefficient estimates , Gaussian hypergeometric functions , Hadamard product (convolution) , harmonic , starlike and convex mappings , Univalent

Rights: Copyright © 2014 Rocky Mountain Mathematics Consortium

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Vol.44 • No. 3 • 2014
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