## 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.)