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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2021 / Cilt: 50 - Sayı: 2

Starlikeness for certain close-to-star functions

R. Kanaga
V. Ravichandran
Sayfa
414–432
Yayın Tarihi
2022-10-18
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Several other radii such as radius of univalence and parabolic starlikeness are shown to be the same as the radius of starlikeness of appropriate order.

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Amaç & Hipotez:We find the radius of starlikeness of order $\alpha$, $0\leq \alpha<1$, of normalized analytic functions $f$ on the unit disk satisfying either $Re(f(z)/g(z))>0$ or $\left|(f(z)/g(z))-1\right|<1$ for some close-to-star function $g$ with $Re(g(z)/(z+z^2/2))>0$ as well as of the class of close-to-star functions $f$ satisfying $Re(f(z)/(z+z^2/2))>0$.
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Temel Bulgular & Veri:We find the radius of starlikeness of order $\alpha$, $0\leq \alpha<1$, of normalized analytic functions $f$ on the unit disk satisfying either $Re(f(z)/g(z))>0$ or $\left|(f(z)/g(z))-1\right|<1$ for some close-to-star function $g$ with $Re(g(z)/(z+z^2/2))>0$ as well as of the class of close-to-star functions $f$ satisfying $Re(f(z)/(z+z^2/2))>0$.
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Sonuç & Katkı:Several other radii such as radius of univalence and parabolic starlikeness are shown to be the same as the radius of starlikeness of appropriate order.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Univalent functions · convex functions · starlike functions

Abstract

We find the radius of starlikeness of order $\alpha$, $0\leq \alpha<1$, of normalized analytic functions $f$ on the unit disk satisfying either $Re(f(z)/g(z))>0$ or $\left|(f(z)/g(z))-1\right|<1$ for some close-to-star function $g$ with $Re(g(z)/(z+z^2/2))>0$ as well as of the class of close-to-star functions $f$ satisfying $Re(f(z)/(z+z^2/2))>0$. Several other radii such as radius of univalence and parabolic starlikeness are shown to be the same as the radius of starlikeness of appropriate order.

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Bu Makaleye Atıf Yap

Kanaga, R., Ravichandran, V. (2022). Starlikeness for certain close-to-star functions. Hacettepe Journal of Mathematics and Statistics, Cilt: 50 - Sayı: 2, 414–432. https://ajindex.com/articles/529960

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Kaynakça (18)

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