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International Journal of Mathematics and Mathematical Sciences
Volume 9, Issue 4, Pages 721-730

An application of the Ruscheweyh derivatives

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

Received 15 January 1986

Copyright © 1986 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Let Dαf(z) be the Ruscheweyh derivative defined by using the Hadamard product of f(z) and z/(1z)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.