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International Journal of Mathematics and Mathematical Sciences
Volume 14, Issue 3, Pages 451-456
http://dx.doi.org/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 Hindawi Publishing Corporation. 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 pβ<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.