International Journal of Mathematics and Mathematical Sciences
Volume 10 (1987), Issue 1, Pages 79-88
doi:10.1155/S0161171287000103

On Bazilevich functions

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.