International Journal of Mathematics and Mathematical Sciences
Volume 2005 (2005), Issue 4, Pages 561-570
doi:10.1155/IJMMS.2005.561

Starlikeness associated with parabolic regions

Abstract

A parabolic starlike function f of order ρ in the unit disk is characterized by the fact that the quantity zf′(z)/f(z) lies in a given parabolic region in the right half-plane. Denote the class of such functions by PS∗(ρ). This class is contained in the larger class of starlike functions of order ρ. Subordination results for PS∗(ρ) are established, which yield sharp growth, covering, and distortion theorems. Sharp bounds for the first four coefficients are also obtained. There exist different extremal functions for these coefficient problems. Additionally, we obtain a sharp estimate for the Fekete-Szegö coefficient functional and investigate convolution properties for PS∗(ρ).