On Booth lemniscate of starlike functions

TL;DR

This paper introduces a new class of starlike functions related to Booth lemniscate, exploring their properties including subordination, coefficient bounds, and inequalities, expanding the understanding of geometric function theory.

Contribution

It defines the class al{BS}(lpha) of functions subordinate to a Booth lemniscate-related function and studies its properties, which is a novel contribution to geometric function theory.

Findings

Established differential subordination properties.

Derived coefficient estimates for functions in al{BS}(lpha).

Proved Fekete-Szeg
53 inequalities for the class.

Abstract

Assume that $\Delta$ is the open unit disk in the complex plane and $\mathcal{A}$ is the class of normalized analytic functions in $\Delta$. In this paper we introduce and study the class \begin{equation*} \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{equation*} where $0\leq\alpha\leq1$ and $\prec$ is the subordination relation. Some properties of this class like differential subordination, coefficients estimates and Fekete-Szeg\"{o} inequality associated with the $k$-th root transform are considered.