On Some Properties of the Operator, Defined on Class of Analytic in the Half-Plane Functions

Abstract

In present paper the properties of the operator introduced by authors, which is defined on special class of n-normalized analytic in the half-plane functions are investigated. This operator is closely related with automorphism of a half-plane. Close connection of this operator with divided difference of n-th order is shown. The fixed points of the operator were found. Some other invariants, related with operator are under consideration.

Keywords

• analytic functions
• automorphism
• divided difference