Uniqueness of the Critical Point of the Conformal Radius: “Method of Déjà vu”

Abstract

© 2018, Pleiades Publishing, Ltd. New conditions are constructed for the critical point of the conformal radius (hyperbolic derivative) to be unique where the mapping function is holomorphic and locally univalent in the unit disk. We use an approach based on the uniqueness research of the univalence conditions depending on the additional parameters. Such a research has been carried out for the univalence criteria due to Singhs, Szapiel and some other mathematicians.