Bounded functions starlike with respect to symmetrical points

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.