Sharp starlike and convex radius for the differential operator of analytic functions - Hu, Zhenyong; Srivastava, H. M.; Zhang, Ying (Ukrains’kyi Matematychnyi Zhurnal, 2025)
UDC 517.5Under given coefficient conditions for analytic functions $f$ in the unit disk $D$, we first obtain the starlike and convex radius for the linear combination of the differential operator $zf'$ of analytic functions $f$ in $D.$ Then we obtain the starlike and convex radius for the differential operator $zf'$. Furthermore, we present the starlike and convex radius for the linear combination of the differential operator $zf'$ and analytic functions $f$ in $D$. Our results imply the related result obtained by Gavrilov [Mat. Zametki, 7, 295–298 (1970)].