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Zbl 1222.30011
Noor, Khalida Inayat; Noor, Muhammad Aslam; Al-Said, Eisa A.
On certain analytic functions with bounded radius rotation.
(English)
[J] Comput. Math. Appl. 61, No. 10, 2987-2993 (2011). ISSN 0898-1221

Summary: Certain classes $R_k(\mu,\alpha)$; $k\ge 2$, $\mu>-1$, $0\le\alpha<1$ of analytic functions are defined in the unit disc using convolution technique. It is shown that functions in $R_{k}(\mu ,\alpha )$ are of bounded radius rotation. It is proved that $R_{k}(\mu ,\alpha )$ 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 2000:
*30C45 Special classes of univalent and multivalent functions

Keywords: bounded radius rotation; starlike; linear operator; Ruscheweyh derivative; convolution; functions with positive real part

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