On a subclass of starlike functions associated with a strip domain
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 domai...
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| Datum: | 2025 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2025
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/8000 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | 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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| DOI: | 10.3842/umzh.v76i12.8000 |