A New Roper-Suffridge Extension Operator on a Reinhardt Domain

Abstract

We introduce a new Roper-Suffridge extension operator on the following Reinhardt domain given by where f is a normalized locally biholomorphic function on the unit disc D, pj are positive integer, aj are complex constants, and j=2,…,n. Some conditions for aj are found under which the operator preserves almost starlike mappings of order α and starlike mappings of order α, respectively. In particular, our results reduce to many well-known results when all αj=0.