International Journal of Mathematics and Mathematical Sciences
Volume 9 (1986), Issue 4, Pages 721-730
doi:10.1155/S0161171286000868

An application of the Ruscheweyh derivatives

Shigeyoshi Owa1 , Seiichi Fukui2 , Koichi Sakaguchi3 and Shotaro Ogawa1

1Department of Mathematics, Kinki University, Higashi-Osaka, Osaka 577, Japan
 2Department of Mathematics, Wakayama University, Wakayama 640, Japan
 3Department of Mathematics, Nara University of Education, Nara 630, Japan

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.