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An application of the Ruscheweyh derivatives. (English) Zbl 0613.30013

Let \(D^{\alpha}f(z)\) be the Ruscheweyh derivative defined by using the Hadamard product of f(z) and \(z/(1-z)^{1+\alpha}\). Certain new classes \(S^*_{\alpha}\) and \(K_{\alpha}\) are introduced by virtue of the Ruscheweyh derivative. The object of the present paper is to establish several interesting properties of \(S^*_{\alpha}\) and \(K_{\alpha}\) (see the review below). Further, some results for integral operator \(J_ c(f)\) of f(z) are shown.

MSC:

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

Citations:

Zbl 0613.30014
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