International Journal of Mathematics and Mathematical Sciences
Volume 10 (1987), Issue 1, Pages 79-88
doi:10.1155/S0161171287000103
On Bazilevic functions
Mathematics Department, Girls College of Education, (Science Section) Sitteen Road, Malaz, Riyadh, Saudi Arabia
Received 23 January 1985; Revised 28 June 1986
Copyright © 1987 Khalida I. Noor and Sumayya A. Al-Bany. 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
Let B(β) be the class of Bazilevic functions of type β(β>0). A function f ϵ B(β) if it is analytic in the unit disc E and Rezf′(z)f1−β(z)gβ(z)>0, where g is a starlike function. We generalize the class B(β) by taking g to be a function of radius rotation at most kπ(k≥2). Archlength, difference of coefficient, Hankel determinant and some other problems are solved for this generalized class. For k=2, we obtain some of these results for the class B(β) of Bazilevic functions of type β.