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

Helge Glockner
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Abstract

We 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.

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Helge Glockner. 2007-04-27. Finite order differentiability properties, fixed points and implicit functions over valued fields. https://arxiv.org/abs/math/0511218

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