Earle–Hamilton fixed-point theorem: Difference between revisions

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In [[mathematics]], the '''Earle–Hamilton fixed point theorem''' is a result in [[geometric function theory]] giving sufficient conditions for a [[holomorphic mapping]] of an open ___domain in a complex [[Banach space]] into itself to have a fixed point. The result was proved in 1968 by Clifford Earle and [[Richard Hamilton (mathematician)|RichardS. Hamilton]] by showing that, with respect to the [[Carathéodory metric]] on the ___domain, the holomorphic mapping becomes a [[contraction mapping]] to which the [[Banach fixed-point theorem]] can be applied.

==Statement==

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==References==

*{{citation|lastlast1=Earle|firstfirst1= Clifford J.|last2=Hamilton|first2= Richard S.|

title=A fixed point theorem for holomorphic mappings|year= 1970|series=Proc. Sympos. Pure Math.|volume= XVI|pages= 61–65|publisher =American MathemeticalMathematical Society}}

*{{citation|last=Harris|first= Lawrence A.|title=Fixed points of holomorphic mappings for domains in Banach spaces|journal=Abstr. Appl. Anal.|year= 2003|volume= 5| pages=261–274|url=http://www.hindawi.com/journals/aaa/2003/121329/abs/}}

*{{citation|last=Neretin|first= Y. A.|title=Categories of symmetries and infinite-dimensional groups|series= London Mathematical Society Monographs|volume=16|publisher= Oxford University Press|year= 1996|isbn=0-19-851186-8}}

*{{citation|last=Clerc|first=Jean-Louis|title=Compressions and contractions of Hermitian symmetric spaces|journal=Math. Z.|volume= 229|year=1998|pages=1–8|url=http://www.springerlink.com/content/29yxnqe2ph9y4hhk/|doi=10.1007/pl00004648|s2cid=122333415}}

{{DEFAULTSORT:Earle-Hamilton fixed-point theorem}}