Injectivity and univalence of complex functions via monotonicity

2013/10/24 by Szilárd Csaba László, Szilárd László, László, Szilárd
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #Functional Equations Stability Results #Mathematical Inequalities and Applications #Mathematical functions and polynomials #math.FA

paper · pdf · doi:10.48550/arxiv.1310.6703

arxiv created 2013/10/24 · openalex publication_date 2013/10/24 · arxiv updated 2013/10/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we provide sufficient conditions that ensure the monotonicity, respectively the global injectivity of an operator. Further, some new analytical conditions that assure the injectivity/univalence of a complex function of one complex variable are obtained. We also show that some classical results, such as Alexander-Noshiro-Warschawski and Wolff theorem or Mocanu theorem, are easy consequences of our results.

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