On a subfamily of starlike functions related to Hyperbolic Cosine function

TL;DR

This paper introduces a new subclass of starlike functions defined via the hyperbolic cosine function, establishing inclusion relations and sharp radii for subclasses, advancing geometric function theory.

Contribution

It defines a novel Ma-Minda subclass related to the hyperbolic cosine and derives key properties and radii, expanding the understanding of starlike functions.

Findings

Established inclusion relations for the new subclass.

Derived sharp radii for specific subclasses.

Connected the subclass to classical geometric function theory.

Abstract

We introduce and study a new Ma-Minda subclass of starlike functions $\mathcal{S}^*_{\varrho},$ defined as $$\mathcal{S}^{*}_{\varrho}:=\left\{f\in\mathcal{A}:\frac{zf'(z)}{f(z)} \prec \cosh \sqrt{z}=:\varrho(z), z\in\mathbb{D} \right\},$$ associated with an analytic univalent function $\cosh \sqrt{z},$ where we choose the branch of the square root function so that $\cosh\sqrt{z}=1+z/2!+z^{2}/{4!}+\cdots.$ We establish certain inclusion relations for $\mathcal{S}^{*}_{\varrho}$ and deduce sharp $\mathcal{S}^{*}_{\varrho}-$radii for certain subclasses of analytic functions.