A New Operator for Meromorphic Functions

Abstract

Let Σ be the class of functions f(z) of the form f(z)=1z+∑k=0∞akzk, which are analytic in the punctured disk. Using the differentiations and integrations, new operator Dnf(z) is introduced for f(z)∈Σ. The object of the present paper is to discuss some interesting properties for Dnf(z) and some properties concerned with different boundary points of the open unit disk. Moreover, some simple examples for our results are shown.