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Zbl 0942.30007
Noor, Khalida Inayat
On new classes of integral operators.
(English)
[J] J. Nat. Geom. 16, No.1-2, 71-80 (1999). ISSN 0963-2654

Let ${\cal A}$ be the class of normalized functions $f(z) = z + a_{2}z^{2} + \dots,$ analytic in the unit disk, and let $S ^{*} \subset {\cal A}$ be the class of starlike functions. The author considers the classes $N ^{*} (n) = D ^{n} S ^{*}$, where $D^{n}f = z (1-z)^{-n-1}*f(z),$ $n=0,1,\dots$, is the Ruscheweyh derivative. \par Coefficient estimates and some inclusion and radius results are obtained for these classes. There are several misprints in the paper, for instance, $N ^{*} (1) \neq S ^{*},$ moreover, if $n>0$, then $N ^{*}(n)$ contains non-univalent functions.
[Iskander Nezhmetdinov (Chennai)]
MSC 2000:
*30C45 Special classes of univalent and multivalent functions

Keywords: Ruscheweyh derivative; starlike functions; coefficient estimates

Cited in: Zbl 1096.30008 Zbl 1035.30004

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