International Journal of Mathematics and Mathematical Sciences
Volume 7 (1984), Issue 4, Pages 719-730

On new classes of analytic functions with negative coefficients

Shigeyoshi Owa

Department of Mathematics, Faculty of Science and Technology, Kinki University, Higashi-Osaka, Osaka, Japan

Received 11 November 1983

Copyright © 1984 Shigeyoshi Owa. 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.


We introduce the classes Kn* of analytic functions with negative coefficients by using the nth order Ruscheweyh derivative. The object of the present paper is to show coefficient inequalities and some closure theorems for functions f(z) in Kn*. Further we consider the modified Hadamard product of functions fi(z) in Kni*(n=1,2,,m).