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 517.5 Under 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)].