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.
Publié le : 2007-12-14
Classification:
Levi-Civita field,
non-Archimedean analysis,
power series,
analytic functions,
intermediate value theorem,
12J25,
26E30,
30G06,
46S10
@article{1197908910,
author = {Shamseddine, Khodr and Berz, Martin},
title = {Intermediate Value Theorem for Analytic Functions on a Levi-Civita Field},
journal = {Bull. Belg. Math. Soc. Simon Stevin},
volume = {13},
number = {5},
year = {2007},
pages = { 1001-1015},
language = {en},
url = {http://dml.mathdoc.fr/item/1197908910}
}
Shamseddine, Khodr; Berz, Martin. Intermediate Value Theorem for Analytic Functions on a Levi-Civita Field. Bull. Belg. Math. Soc. Simon Stevin, Tome 13 (2007) no. 5, pp. 1001-1015. http://gdmltest.u-ga.fr/item/1197908910/