Coefficient Conditions for Harmonic Univalent Mappings and Hypergeometric Mappings
Complex Variables
2012-06-05 v2
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.
Cite
@article{arxiv.1109.0925,
title = {Coefficient Conditions for Harmonic Univalent Mappings and Hypergeometric Mappings},
author = {S. V. Bharanedhar and S. Ponnusamy},
journal= {arXiv preprint arXiv:1109.0925},
year = {2012}
}
Comments
This was presented in a meeting in August 2010 and this has now been accepted to appear in Rocky Mountain Journal of Mathematics