Starlikeness for certain close-to-star functions

Year 2021, Volume: 50 Issue: 2, 414 - 432, 11.04.2021

R. Kanaga V Ravichandran

https://doi.org/10.15672/hujms.702703

Cited By: 5

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.

Keywords

Univalent functions, convex functions, starlike functions, subordination, radius of starlikeness

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