Bulletin of the Belgian Mathematical Society - Simon Stevin

Intermediate Value Theorem for Analytic Functions on a Levi-Civita Field

Martin Berz and Khodr Shamseddine

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Abstract

The proof of the intermediate value theorem for power series on a Levi-Civita 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.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 14, Number 5 (2007), 1001-1015.

Dates
First available in Project Euclid: 17 December 2007

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1197908910

Digital Object Identifier
doi:10.36045/bbms/1197908910

Mathematical Reviews number (MathSciNet)
MR2379004

Zentralblatt MATH identifier
1181.26044

Subjects
Primary: 12J25: Non-Archimedean valued fields [See also 30G06, 32P05, 46S10, 47S10] 26E30: Non-Archimedean analysis [See also 12J25]
Secondary: 30G06: Non-Archimedean function theory [See also 12J25]; nonstandard function theory [See also 03H05] 46S10: Functional analysis over fields other than $R$ or $C$ or the quaternions; non-Archimedean functional analysis [See also 12J25, 32P05]

Keywords
Levi-Civita field non-Archimedean analysis power series analytic functions intermediate value theorem

Citation

Shamseddine, Khodr; Berz, Martin. Intermediate Value Theorem for Analytic Functions on a Levi-Civita Field. Bull. Belg. Math. Soc. Simon Stevin 14 (2007), no. 5, 1001--1015. doi:10.36045/bbms/1197908910. https://projecteuclid.org/euclid.bbms/1197908910


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