On certain meromorphic p-valent starlike functions

A certain differential operator Dn+p is introduced for functions of the form f ( z ) = 1 z p + a 0 z p - 1 + ⋯ + a k + p - 1 z k + ⋯ which are regular in the annulus E * = { z ∈ C : 0 < | z | < 1 } , where p is a positive integer. The main object of this paper is to give an application of the operator Dn+p to the differential inequalities.