International Journal of Mathematics and Mathematical Sciences
Volume 19 (1996), Issue 3, Pages 615-623

Bounded functions starlike with respect to symmetrical points

Fatima M. Al-Oboudi

Department of Mathematics, Girls College of Education, Sitteen Street, Malaz, Riyadh, Saudi Arabia

Received 28 September 1994; Revised 7 March 1995

Copyright © 1996 Fatima M. Al-Oboudi. 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.


Let P[A,B], 1B<A1, be the class of functions p analytic in the unit disk E with p(0)=1 and subordinate to 1+Az1+Bz. In this paper we define and study the classes SS*[A,B] of functions starlike with respect to symmetrical points. A function f analytic in E and given by f(z)=z+n=2anzn is said to be in SS*[A,B] if and only if, for zE, 2zf(z)f(z)f(z)P[A,B]. Basic results on SS*[A,B] are studied such as coefficient bounds, distortion and rotation theorems, the analogue of the Polya-Schoenberg conjecture and others.