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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.