A New Operator for Meromorphic Functions

Let S be the class of functions f ( z) of the form f ( z) = 1/z + Sigma(infinity)(k =0)a(k)z(k), which are analytic in the punctured disk. Using the differentiations and integrations, new operator D-n f (z) is introduced for f (z) is an element of Sigma. The object of the present paper is to discuss some interesting properties for D-n f (z) and some properties concerned with different boundary points of the open unit disk. Moreover, some simple examples for our results are shown.