On Injectivity of a Class of Monotone Operators with Some Univalency Consequences

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• 作者：Szilárd László
• 关键词：Monotone operator ; convex preimage ; injective operator ; complex function ; univalent function
• 刊名：Mediterranean Journal of Mathematics
• 出版年：2016
• 出版时间：April 2016
• 年：2016
• 卷：13
• 期：2
• 页码：729-744
• 全文大小：550 KB
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• 作者单位：Szilárd László (1)
  
  1. Department of Mathematics, Technical University of Cluj-Napoca, Str. Memorandumului nr. 28, 400114, Cluj-Napoca, Romania
  
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Mathematics
  
• 出版者：Birkh盲user Basel
• ISSN：1660-5454

文摘

In this paper, we provide sufficient conditions that ensure the convexity of the inverse images of an operator, monotone in some sense. Further, conditions that ensure the monotonicity, respectively the local injectivity of an operator, are also obtained. Combining the conditions that provide the local injectivity, respectively the convexity of the inverse images of an operator, we are able to obtain some global injectivity results. As applications, some new analytical conditions that assure the injectivity, respectively univalency 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.