An application of the Ruscheweyh derivatives

Abstract

Let Dαf(z) be the Ruscheweyh derivative defined by using the Hadamard product of f(z) and z/(1−z)1+α. Certain new classes Sα* and Kα are introduced by virtue of the Ruscheweyh derivative. The object of the present paper is to establish several interesting properties of Sα* and Kα. Further, some results for integral operator Jc(f) of f(z) are shown.

Keywords

• Ruscheweyh derivative
• Hadamard product
• starlike function
• convex function
• integral operator.