A CLASS OF ANALYTIC FUNCTIONS DEFINED BY THE CARLSON-SHAFFER OPERATOR

摘要

The Carlson-Shaffer operator L(a,c)f = Φ(a,c) * f, where f(z) = z + a_2z~2 +…is analytic in the unit disk E = {z : |z| < 1} and Φ(a, c; z) is an incomplete beta function, is used to define the class T(a,c). An analytic function f belongs to T(a,c) if L(a,c)f is starlike in E. The object of the present paper is to derive some properties of functions f in the class T(a,c).