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On Locally Uniformly Differentiable Functions on a Complete Non-Archimedean Ordered Field Extension of the Real Numbers
Joint Authors
Shamseddine, Khodr
Sierens, Todd
Source
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-20, 20 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-04-17
Country of Publication
Egypt
No. of Pages
20
Main Subjects
Abstract EN
We 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.
American Psychological Association (APA)
Shamseddine, Khodr& Sierens, Todd. 2012. On Locally Uniformly Differentiable Functions on a Complete Non-Archimedean Ordered Field Extension of the Real Numbers. ISRN Mathematical Analysis،Vol. 2012, no. 2012, pp.1-20.
https://search.emarefa.net/detail/BIM-468101
Modern Language Association (MLA)
Shamseddine, Khodr& Sierens, Todd. On Locally Uniformly Differentiable Functions on a Complete Non-Archimedean Ordered Field Extension of the Real Numbers. ISRN Mathematical Analysis No. 2012 (2012), pp.1-20.
https://search.emarefa.net/detail/BIM-468101
American Medical Association (AMA)
Shamseddine, Khodr& Sierens, Todd. On Locally Uniformly Differentiable Functions on a Complete Non-Archimedean Ordered Field Extension of the Real Numbers. ISRN Mathematical Analysis. 2012. Vol. 2012, no. 2012, pp.1-20.
https://search.emarefa.net/detail/BIM-468101
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-468101