Loewner chains applied to g-starlike mappings of complex order of complex Banach spaces

Abstract

This paper is devoted to studying geometric and analytic properties of g - starlike mappings of complex order λ . By using Loewner chains, we obtain the growth theorems for g -starlike mappings of complex order λ on the unit ball in reflexive complex Banach spaces, which generalize some results of Graham, Hamada and Kohr. As applications, several different kinds of distortion theorems for g -starlike mappings of complex order λ are obtained. Finally, we prove that the Roper–Suffridge extension operators preserve the property of g -starlike mappings of complex order λ in complex Banach spaces, which generalizes many classical results.