Coefficient Conditions for Harmonic Univalent Mappings and Hypergeometric Mappings

Details Coefficient Conditions for Harmonic Univalent Mappings and Hypergeometric Mappings Coefficient Conditions for Harmonic Univalent Mappings and Hypergeometric Mappings

2011-09-05

arxiv.org/abs/1109.0925v1

Mathematics

Complex Variables

This was presented in a meeting in August 2010

Scientific paper

In this paper, we obtain coefficient criteria for a normalized harmonic function defined in the unit disk to be close-to-convex and starlike, respectively. Using these coefficient conditions, we present different classes of harmonic close-to-convex (resp. starlike) functions involving the Gaussian hypergoemetric 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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