Ruscheweyh's univalence criterion and quasiconformal extensions

2009/10/25 by Hotta, Ikkei
#30C45 #30C62 #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.0910.4744

Abstract

Ruscheweyh extended the work of Becker and Ahlfors on sufficient conditions for a normalized analytic function on the unit disk to be univalent there. In this paper we refine the result to a quasiconformal extension criterion with the help of Becker's method. As an application, a positive answer is given to an open problem proposed by Ruscheweyh.

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• Univalence Criteria and Quasiconformal Extensions
• Ahlfors's quasiconformal extension condition and Φ-likeness
• Sufficient conditions for univalence of analytic functions
• Univalent functions with quasiconformal extensions: Becker's class and estimates of the third coefficient
• Univalence and quasiconformal extension of an integral operator