Finite order differentiability properties, fixed points and implicit functions over valued fields

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dc.creatorGlockner, Helge
dc.date2005-11-08
dc.date2007-04-27
dc.date.accessioned2026-07-07T07:58:25Z
dc.date.available2026-07-07T07:58:25Z
dc.descriptionWe prove an implicit function theorem for C^k-maps from arbitrary topological vector spaces over valued fields to Banach spaces (for k at least 2). As a tool, we show the C^k-dependence of fixed points on parameters for suitable families of contractions of a Banach space. Similar results are obtained for k times strictly differentiable maps, and for k times Lipschitz differentiable maps. In the real case, our results subsume an implicit function theorem for Keller C^k_c-maps from arbitrary topological vector spaces to Banach spaces.
dc.descriptionLaTeX, 59 pages, broadly written preprint (v2: new Appendix C extends C^1-case from locally compact fields to complete valued fields)
dc.identifierhttps://arxiv.org/abs/math/0511218
dc.identifierhttp://arxiv.org/abs/math/0511218
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/128001
dc.subjectFunctional Analysis
dc.subjectGeneral Mathematics
dc.subject58C15; 47H10; 26E30; 58C20; 46S10; 26E15; 26E20
dc.titleFinite order differentiability properties, fixed points and implicit functions over valued fields
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