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arXiv · 2103.10140

On a subclass of close-to-convex harmonic mappings

Manivannan Mathi·Jugal Kishore Prajapat
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Abstract

For $\alpha > -1$ and $\beta >0, $ let $\mathcal{B}_{\mathcal{H}}^0(\alpha, \beta)$ denote the class of sense preserving harmonic mappings $f=h+\overline{g}$ in the open unit disk $\mathbb{D}$ satisfying $|zh''(z)+\alpha(h'(z)-1)|\leq \beta-|zg''(z)+\alpha g'(z)|.$ First, we establish that each function belonging to this class is close-to-convex in the open unit disk if $\beta \in (0, 1+\alpha]$. Next, we obtain coefficient bounds, growth estimates and convolution properties. We end the paper with applications and will construct harmonic univalent polynomials belonging to this class.

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Manivannan Mathi, Jugal Kishore Prajapat. 2021-03-18. On a subclass of close-to-convex harmonic mappings. https://arxiv.org/abs/2103.10140

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