# Integral operators that preserve the subordination

• Bulboaca, Teodor (Faculty of Mathematics and Computer Science, Babes-Bolyai University)
• Published : 1997.11.01

#### Abstract

Let $H(U)$ be the space of all analytic functions in the unit disk $U$ and let $K \subset H(U)$. For the operator $A_{\beta,\gamma} : K \longrightarrow H(U)$ defined by $$A_{\beta,\gamma}(f)(z) = [\frac{z^\gamma}{\beta + \gamma} \int_{0}^{z} f^\beta (t)t^{\gamma-1} dt]^{1/\beta}$$ and $\beta,\gamma \in C$, we determined conditions on g(z), $\beta and \gamma$ such that $$z[\frac{z}{f(z)]^\beta \prec z[\frac{z}{g(z)]^\beta implies z[\frac{z}{A_{\beta,\gamma}(f)(z)]^\beta \prec z[\frac{z}{A_{\beta,\gamma}(g)(z)]^\beta$$ and we presented some particular cases of our main result.

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