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On certain analytic functions with bounded radius rotation. (English) Zbl 1222.30011
Summary: Certain classes ${R}_{k}\left(\mu ,\alpha \right)$; $k\ge 2$, $\mu >-1$, $0\le \alpha <1$ of analytic functions are defined in the unit disc using convolution technique. It is shown that functions in ${R}_{k}\left(\mu ,\alpha \right)$ are of bounded radius rotation. It is proved that ${R}_{k}\left(\mu ,\alpha \right)$ and some other newly introduced related classes are invariant under the generalized Bernardi integral operator. The converse case as a radius problem is also considered. Theorems proved in this paper are best possible in some sense.
##### MSC:
 30C45 Special classes of univalent and multivalent functions
##### References:
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