Coefficient conditions for harmonic univalent mappings and hypergeometric mappings
S.V. Bharanedhar, S. Ponnusamy
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Source: Crossref
Published: Jun 1, 2014
DOI: 10.1216/rmj-2014-44-3-753
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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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