On a subclass of starlike functions associated with a strip domain

S. Sivaprasad Kumar; Neha Verma

doi:10.3842/umzh.v76i12.8000

S. Sivaprasad Kumar Department of Applied Mathematics, Delhi Technological University, Shahbad Daulatpur, India
Neha Verma Department of Applied Mathematics, Delhi Technological University, Shahbad Daulatpur, India

DOI: https://doi.org/10.3842/umzh.v76i12.8000

Keywords: Starlike function, Strip domain, Coefficient estimate, Hankel determinant

Abstract

UDC 517.5

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

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