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arXiv · 1109.0925

Coefficient Conditions for Harmonic Univalent Mappings and Hypergeometric Mappings

S. V. Bharanedhar·S. Ponnusamy
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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 (resp. 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 provide examples of harmonic polynomials that are close-to-convex and starlike, respectively.

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S. V. Bharanedhar, S. Ponnusamy. 2011-09-05. Coefficient Conditions for Harmonic Univalent Mappings and Hypergeometric Mappings. https://arxiv.org/abs/1109.0925

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