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
School of Mathematical Sciences, Universiti Sains Malaysia, Penang 11800, Malaysia
Received 29 April 2004; Revised 15 September 2004
Copyright © 2005 Rosihan M. Ali. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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).