International Journal of Mathematics and Mathematical Sciences
Volume 32 (2002), Issue 5, Pages 271-280
doi:10.1155/S016117120220335X

On a class of meromorphic p-valent starlike functions involving certain linear operators

Jin-Lin Liu1 and Shigeyoshi Owa2

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.

Abstract

Let ∑p be the class of functions f(z) which are analytic in the punctured disk 𝔼*={z∈ℂ:0<|z|<1}. Applying the linear operator Dn+p defined by using the convolutions, the subclass 𝒯n+p(α) of ∑p is considered. The object of the present paper is to prove that 𝒯n+p(α)⊂𝒯n+p−1(α). Since 𝒯0(α) is the class of meromorphic p-valent starlike functions of order α, all functions in 𝒯n+p−1(α) are meromorphic p-valent starlike in the open unit disk 𝔼. Further properties preserving integrals and convolution conditions are also considered.