**General Mathematics, Vol. 4, 1996 **

**Abstract:** Let ${\cal U}$ be the open complex unit disc and let ${\cal A}$ be the
class of all functions $f$, analytic in ${\cal U}$ and normed with the conditions
$f(0)=0$, $f'(0)=1$. Let ${\cal B}$ be the class of all analytic functions $h$, defined on
${\cal U}$ and with $h(0)=1$. If $\gamma$ is a real number, greated then $-1$ and $g\in
{\cal A}$, $h\in {\cal B}$, we define the integral operator\\ $I_{g,h}:{\cal A}\rightarrow
{\cal A}$ by $F(z)={\cal I}(f)(z)$, where: \[ F(z)=\frac{\gamma
+1}{g^{\gamma}(z)}\int\limits_{0}^{z}f(u)g^{\gamma -1}(u)h(u)du\ \ \ ,\ \ \ z\in {\cal U}\
. \] If ${\cal R}=\{f\in {\cal A}:Re\, f'(z)>0,z\in {\cal U}\}$ is the class of
functions with bounded rotation in ${\cal U}$ and $S^{\ast}=\displaystyle{\left\{f\in
{\cal A}:\frac{Re\, zf'(z)}{f(z)}>0,z\in {\cal U}\right\}}$ is the class of starlike
functions in ${\cal U}$, we will obtain sufficient conditions on $\gamma ,g$ and $h$ so
that ${\cal I}_{g,h}({\cal R})\subset S^{\ast}$.

**Classification (MSC91): 30C42**

**Keywords:** bounded rotation, convexity of order alpha, starlike function,
subordination.

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