Univalent function: Difference between revisions

Revision as of 21:36, 31 August 2022

Revision as of 21:46, 31 August 2022

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{{other uses|Univalent}}

{{Merge to|Injective function|discuss=Talk:Injective function#Proposed merge of Univalent function into Injective function|date=August 2022}}

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In [[mathematics]], in the branch of [[complex analysis]], a [[holomorphic function]] on an [[open subset]] of the [[complex plane]] is called '''univalent''' if it is [[Injective function|injective]].<ref>[[John B. Conway]] (1996) ''Functions of One Complex Variable II'', chapter 14: Conformal equivalence for simply connected regions, page 32, Springer-Verlag, New York, {{ISBN|0-387-94460-5}}. Definition 1.12: "A function on an open set is ''univalent'' if it is analytic and one-to-one."</ref><ref>{{Cite book |last=Nehari |first=Zeev |url=https://www.worldcat.org/oclc/1504503 |title=Conformal mapping |date=1975 |publisher=Dover Publications |isbn=0-486-61137-X |___location=New York |oclc=1504503|p=146}}</ref>

== Examples==