The Generalized Roper-Suffridge Extension Operator on the Reinhardt Domain, By Hossein Piri

Research

Title	The Generalized Roper-Suffridge Extension Operator on the Reinhardt Domain
Type	Article
Keywords	Roper-Suffridge extension operator, Reinhardt Domain, Almost spirallike mapping of type β and order α, Spirallike mapping of type β and order α, Minkowski functional.
Researchers	Samira Rahrovi، Hossein Piri

Abstract

Let jp∈ and 1jp≥, 2jn=,, be a fixed positive integer. In this paper a generalized Roper-Suffridgeextension operator 112111212()()()()(())(())ppnnjjnjFzfzfzPzfzzfzz=′′′=+,,,,Σ on Reinhardt domain 22…12{1}jnnpnnppjjzzz,,,=Ω=∈:||+||<Σ is defined. Some different conditions forjP are established under which the operator preserves an almost spirallike mapping of type β and order α and spirallike mapping of type β and order α, respectively. In particular, our results reduce to many well-known results.