ON SPIRALLIKE INTEGRAL OPERATORS

Abstract

In this paper the integral operators

\[ F(z)=\left[\frac{\beta+\gamma}{z^\gamma}\int_0^z [f(t)]^\beta t^{\gamma-1} dt\right]^{1/\beta}\]

for $f(z) \in S^\alpha(\lambda, a, b)$ are studied. $S^\alpha(\lambda, a, b)$ as a subclass of the class of all spirallike functions was introduced and studied by the authors. It is shown that $F(z)$ is also in $S^\alpha(\lambda, a, b)$, whenever $f(z)$ is in $S^\alpha(\lambda, a, b)$, under certain restrictions.