On Locally Uniformly Differentiable Functions on a Complete Non-Archimedean Ordered Field Extension of the Real Numbers

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dc.contributor.authorShamseddine, Khodr
dc.contributor.authorSierens, Todd
dc.date.accessioned2015-05-14T16:37:23Z
dc.date.available2015-05-14T16:37:23Z
dc.date.issued2012-4-17
dc.date.updated2015-03-29T13:32:42Z
dc.description.abstractWe study the properties of locally uniformly differentiable functions on 𝒩, a non-Archimedean field extension of the real numbers that is real closed and Cauchy complete in the topology induced by the order. In particular, we show that locally uniformly differentiable functions are 𝐶1, they include all polynomial functions, and they are closed under addition, multiplication, and composition. Then we formulate and prove a version of the inverse function theorem as well as a local intermediate value theorem for these functions.
dc.description.versionPeer Reviewed
dc.identifier.citationKhodr Shamseddine and Todd Sierens, “On Locally Uniformly Differentiable Functions on a Complete Non-Archimedean Ordered Field Extension of the Real Numbers,” ISRN Mathematical Analysis, vol. 2012, Article ID 387053, 20 pages, 2012. doi:10.5402/2012/387053
dc.identifier.urihttp://dx.doi.org/10.5402/2012/387053
dc.identifier.urihttp://hdl.handle.net/1993/30500
dc.language.rfc3066en
dc.rightsopen accessen_US
dc.rights.holderCopyright © 2012 Khodr Shamseddine and Todd Sierens. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
dc.titleOn Locally Uniformly Differentiable Functions on a Complete Non-Archimedean Ordered Field Extension of the Real Numbers
dc.typeJournal Article
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