Stable geometrical properties of logharmonic mappings

Abstract

In this paper, we consider logharmonic mappings which are stable univalent, stable starlike, stable with positive real part, stable close to starlike and stable typically real. We prove that the mappings are starlike logharmonic (resp. logharmonic univalent, close to starlike logharmonic, typically real logharmonic) for all if and only if the mappings are starlike analytic (resp. analytic univalent, close to starlike analytic, typically real analytic) for all . We also prove growth distortion theorems for these family of functions.