On a Subclass of Starlike Functions Associated with a Strip Domain

TL;DR

This paper introduces a new subclass of starlike functions associated with a strip domain, deriving structural, growth, distortion theorems, and establishing inclusion relations, radius estimates, and coefficient bounds.

Contribution

It defines a novel subclass of starlike functions linked to a strip domain and provides comprehensive structural, geometric, and coefficient estimates.

Findings

Derived structural formulae for the new subclass.

Established growth and distortion theorems.

Obtained sharp coefficient bounds and radius estimates.

Abstract

In the present investigation, we introduce a new subclass of starlike functions defined by $\mathcal{S}^{*}_{\tau}:=\{f\in \mathcal{A}:zf'(z)/f(z) \prec 1+\arctan z=:\tau(z)\}$, where $\tau(z)$ maps the unit disk $\mathbb {D}:= \{z\in \mathbb{C}:|z|<1\}$ onto a strip domain. We derive structural formulae, growth, and distortion theorems for $\mathcal{S}^{*}_{\tau}$. Also, inclusion relations with some well-known subclasses of $\mathcal{S}$ are established and obtain sharp radius estimates, as well as sharp coefficient bounds for the initial five coefficients and the second and third-order Hankel determinants of $\mathcal{S}^{*}_{\tau}$.