International Journal of Mathematics and Mathematical Sciences
Volume 32 (2002), Issue 5, Pages 271-280
On a class of meromorphic -valent starlike functions involving certain linear operators
1Department of Mathematics, Yangzhou University, Jiangsu, Yangzhou 225002, China
2Department of Mathematics, Kinki University, Osaka, Higashi-Osaka 577-8502, Japan
Received 10 March 2002
Copyright © 2002 Jin-Lin Liu and 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.
Let be the class of functions which are analytic in the punctured disk . Applying the linear operator defined by
using the convolutions, the subclass of is considered. The object of the present paper is to prove that . Since is the class of meromorphic -valent starlike functions of order
, all functions in are meromorphic -valent starlike in the open unit disk
. Further properties preserving integrals and
convolution conditions are also considered.