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On new classes of integral operators. (English) Zbl 0942.30007

Let \({\mathcal A}\) be the class of normalized functions \(f(z) = z + a_{2}z^{2} + \dots,\) analytic in the unit disk, and let \(S ^{*} \subset {\mathcal A}\) 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.
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.

MSC:

30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
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