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ARPN Journal of Science and Technology >> Volume 7, Issue 1, January 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



Abstract

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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