A local mean value theorem for functions on non-archimedean field extensions of the real numbers

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Abstract

In this paper, we review the definition and 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. Then we define and study n-times locally uniform differentiable functions at a point or on a subset of N. In particular, we study the properties of twice locally uniformly differentiable functions and we formulate and prove a local mean value theorem for such functions.

Keywords

non-Archimedean calculus non-Archimedean ordered field locally uniformly differentiable functions inverse function theorem intermediate value theorem mean value theorem 

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Copyright information

© Pleiades Publishing, Ltd. 2016

Authors and Affiliations

  1. 1.Department of Physics and AstronomyUniversity of Manitoba WinnipegManitobaCanada

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