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

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.