Starlikeness for certain close-to-star functions

Authors : R. KANAGA, V RAVİCHANDRAN

Pages : 414-432

Doi:10.15672/hujms.702703

View : 15 | Download : 7

Publication Date : 2021-04-11

Article Type : Research Paper

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 $Reinsert ignore into journalissuearticles values(finsert ignore into journalissuearticles values(z);/ginsert ignore into journalissuearticles values(z););>0$ or $\left|insert ignore into journalissuearticles values(finsert ignore into journalissuearticles values(z);/ginsert ignore into journalissuearticles values(z););-1\right|<1$ for some close-to-star function $g$ with $Reinsert ignore into journalissuearticles values(ginsert ignore into journalissuearticles values(z);/insert ignore into journalissuearticles values(z+z^2/2););>0$ as well as of the class of close-to-star functions $f$ satisfying $Reinsert ignore into journalissuearticles values(finsert ignore into journalissuearticles values(z);/insert ignore into journalissuearticles values(z+z^2/2););>0$. 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