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 D n + p defined by using the convolutions, the subclass 𝒯 n + p ( α ) of ∑ p is considered. The object of the present paper is to prove that 𝒯 n + p ( α ) ⊂ 𝒯 n + p − 1 ( α ) . Since 𝒯 0 ( α ) is the class of meromorphic p -valent starlike functions of order α , all functions in 𝒯 n + p − 1 ( α ) are meromorphic p -valent starlike in the open unit disk 𝔼 . Further properties preserving integrals and convolution conditions are also considered.