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On Booth lemniscate and starlike functions

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Abstract

Let \(\Delta \) be the open unit disk in the complex plane and \(\mathcal {A}\) be the class of normalized analytic functions in \(\Delta \). In this paper, we introduce and study the class

$$\begin{aligned} \mathcal {BS}(\alpha ):=\left\{ f\in \mathcal {A}: \left( \frac{zf'(z)}{f(z)}-1\right) \prec \frac{z}{1-\alpha z^2}, \, z\in \Delta \right\} , \end{aligned}$$

where \(0\le \alpha \le 1\) and \(\prec \) is the subordination relation. Some properties of this class like differential subordination, coefficient estimates and Fekete–Szegö inequality associated with the k-th root transform are considered.

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Correspondence to Ali Ebadian.

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Kargar, R., Ebadian, A. & Sokół, J. On Booth lemniscate and starlike functions. Anal.Math.Phys. 9, 143–154 (2019). https://doi.org/10.1007/s13324-017-0187-3

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  • DOI: https://doi.org/10.1007/s13324-017-0187-3

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