Some generalizations on the univalence of an integral operator and quasiconformal extensions

2012/08/13 by Murat Çağlar, Halit Orhan, Çağlar, Murat +1
Mathematics · #30C45 #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Nonlinear Partial Differential Equations #Numerical methods in inverse problems #math.CV #msc:30C45

paper · pdf · doi:10.48550/arxiv.1208.2569

12 pages, submitted to a journal for publication (19 April 2012)

arxiv created 2012/08/13 · openalex publication_date 2012/08/13 · arxiv updated 2012/08/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

By using the method of Loewner chains, we establish some sufficient conditions for the analyticity and univalency of functions defined by an integral operator. Also, we refine the result to a quasiconformal extension criterion with the help of Beckers's method.

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• Some sufficient conditions for the univalence of an integral operator
• Loewner theory for quasiconformal extensions: old and new
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