MODIFIED ROPER-SUFFRIDGE EXTENSION OPERATOR FOR SOME SUBCLASSES OF THE UNIT BALL B^n, By Hossein Piri

Research

Title	MODIFIED ROPER-SUFFRIDGE EXTENSION OPERATOR FOR SOME SUBCLASSES OF THE UNIT BALL B^n
Type	Presentation
Keywords	Roper-Suffridge extension operator, Biholomorphic mapping, Almost starlike mapping.
Researchers	Samira Rahrovi، Hossein Piri

Abstract

Let Q : Cn􀀀1 ! C be a homogenous polynomail of degree 2. We consider the normalized extension of f to the Euclidean unit ball Bn Cn given by [Q(f)](z) = (f(z1) + f′(z1)Q(^z); √ f′(z1)^z); where z = (z1; ^z) 2 Bn. In this paper, we show that under certain conditions, Q(f) preserve almost starlike mappings of complex order .