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arXiv · 1701.07779

On Booth lemniscate of starlike functions

R. Kargar·A. Ebadian·J. Sokół
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Abstract

Assume that $Δ$ is the open unit disk in the complex plane and $\mathcal{A}$ is the class of normalized analytic functions in $Δ$. In this paper we introduce and study the class \begin{equation*} \mathcal{BS}(α):=\left\{f\in \mathcal{A}: \left(\frac{zf'(z)}{f(z)}-1\right)\prec \frac{z}{1-αz^2}, \, z\inΔ\right\}, \end{equation*} where $0\leqα\leq1$ and $\prec$ is the subordination relation. Some properties of this class like differential subordination, coefficients estimates and Fekete-Szegö inequality associated with the $k$-th root transform are considered.

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R. Kargar, A. Ebadian, J. Sokół. 2017-01-26. On Booth lemniscate of starlike functions. https://arxiv.org/abs/1701.07779

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