Intermediate Value Theorem for Analytic Functions on a Levi-Civita Field
نویسندگان
چکیده
The proof of the intermediate value theorem for power series on a LeviCivita field will be presented. After reviewing convergence criteria for power series [19], we review their analytical properties [18]. Then we state and prove the intermediate value theorem for a large class of functions that are given locally by power series and contain all the continuations of real power series: using iteration, we construct a sequence that converges strongly to a point at which the intermediate value will be assumed.
منابع مشابه
Absolute and relative extrema, the mean value theorem and the inverse function theorem for analytic functions on a Levi-Civita field
The proofs of the extreme value theorem, the mean value theorem and the inverse function theorem for analytic functions on the Levi-Civita field will be presented. After reviewing convergence criteria for power series [15], we review their analytical properties [18, 20]. Then we derive necessary and sufficient conditions for the existence of relative extrema for analytic functions and use that ...
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