International Journal of Mathematics and Mathematical Sciences
Volume 19 (1996), Issue 3, Pages 615-623
doi:10.1155/S0161171296000877
Bounded functions starlike with respect to symmetrical points
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.
Abstract
Let P[A,B], −1≤B<A≤1, 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=2∞anzn is said to be in SS*[A,B] if and only if, for z∈E, 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.