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ARPN Journal of Science and Technology >> Volume 7, Issue 2, November 2017

ARPN Journal of Science and Technology

A Fixed Point Theorem for Surfaces

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Author Süheyla Elmas, Seyfullah Hizarci, Abdullah Kaplan
ISSN 2225-7217
On Pages 963-967
Volume No. 2
Issue No. 10
Issue Date December 01, 2012
Publishing Date December 01, 2012
Keywords Fixed point, differential geometry, surface mapping, contraction mapping


The article of this note is to outline a proof of “every homeomorphism of the plane or surface into itself that leaves a continuum M C R^3 invariant has a fixed point in F (M)”. We prove that if F is a Contraction Mapping, then there is at least one fixed point of F, where M C E^2 is a compact surface and F:M ->M is a surface mapping

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