International Journal of Mathematics and Mathematical Sciences
Volume 14 (1991), Issue 3, Pages 451-456
doi:10.1155/S0161171291000613
Functions starlike with respect to other points
S.Abdul Halim
Dept. of Mathematics, University of Malaya, Kuala Lumpur 59100, Malaysia
Abstract
In [7], Sakaguchi introduce the class of functions starlike with respect to symmetric points. We extend this class. For p≤β<1, let SS*(β) be the class of normalised analytic functions f defined in the open unit disc D such that Rezf′(z)/(f(z)−f(−z))>β, for some z ϵ D. In this paper, we introduce 2 other similar classes SC*(β), SSC*(β) as well as give sharp results for the real part of some function for f ϵ SS*(β), SC*(β) and SSC*(β) The behaviour of certain integral operators are also considered.