Let denote the class of functions which are analytic and -valent in the punctured unit disk
For the given real numbers we can define a linear operator
where is a convolution (Hadamard product) and is a special function defined as follows
For the given fixed parameters , , , , , , we say that a function is in the class if it also satisfies the inequality
In this paper some properties of the classes and the operators are investigated. Among others it is proved: Theorem. If , then .