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
Dept. of Mathematics, University of Malaya, Kuala Lumpur 59100, Malaysia
Received 26 September 1990; Revised 5 March 1991
Copyright © 1991 S. Abdul Halim. 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
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.