Rocky Mountain Journal of Mathematics

Coefficient conditions for harmonic univalent mappings and hypergeometric mappings

S.V. Bharanedhar and S. Ponnusamy

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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.

Article information

Rocky Mountain J. Math., Volume 44, Number 3 (2014), 753-777.

First available in Project Euclid: 28 September 2014

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Zentralblatt MATH identifier

Primary: 30C45: Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.)

Harmonic univalent close-to-convex starlike and convex mappings coefficient estimates Gaussian hypergeometric functions Hadamard product (convolution)


Bharanedhar, S.V.; Ponnusamy, S. Coefficient conditions for harmonic univalent mappings and hypergeometric mappings. Rocky Mountain J. Math. 44 (2014), no. 3, 753--777. doi:10.1216/RMJ-2014-44-3-753.

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