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A new class of analytic functions associated with the Ruscheweyh derivatives. (English) Zbl 0621.30010

The object of the present paper is to establish several interesting properties and characteristics of the class \({\mathcal A}_{n,p}(a,b)\) of analytic functions, which is introduced here by using the Ruscheweyh derivatives defined in terms of a certain Hadamard product. A relevant problem associated with the general class \({\mathcal A}_{n,p}(a,b)\) is also proposed. This hitherto unresolved problem would generalize one of the results presented here. Finally, it is shown how the class \({\mathcal A}_{n,p}(a,0)\) is related to a certain generalized integral operator studied, for example, by S. Owa and H. M. Srivastava [ibid. 62, 125-128 (1986; Zbl 0583.30016)].

MSC:

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

Citations:

Zbl 0583.30016
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References:

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