## Coefficient conditions for harmonic univalent mappings and hypergeometric mappings.(English)Zbl 1298.30001

Summary: 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.

### MSC:

 30A05 Monogenic and polygenic functions of one complex variable 30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
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### References:

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