A New Roper‐Suffridge Extension Operator on a Reinhardt Domain

Abstract

We introduce a new Roper-Suffridge extension operator on the following Reinhardt domaingiven bywherefis a normalized locally biholomorphic function on the unit discD,pjare positive integer,ajare complex constants, andj=2,…,n. Some conditions forajare found under which the operator preserves almost starlike mappings of orderαand starlike mappings of orderα, respectively. In particular, our results reduce to many well-known results when allαj=0.