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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
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.
📌 3 Key Takeaways
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Objective & Hypothesis: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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Key Findings & Data: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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Conclusion & Impact: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.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables: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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Cite This Article
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