A new higher order chain rule and Gevrey class

DOI10.1007/BF00128298zbMath0719.58002OpenAlexW1983370645MaRDI QIDQ2640199

Takesi Yamanaka

Publication date: 1989

Published in: Annals of Global Analysis and Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00128298

zbMATH Keywords

generalized derivativesGevrey classinverseimplicit function theoremchain ruleFréchet-differentiable functionGevrey mapsGevrey-type functions

Mathematics Subject Classification ID

Differentiation (real functions of one variable): general theory, generalized derivatives, mean value theorems (26A24) Partial differential equations on manifolds; differential operators (58J99) Derivatives of functions in infinite-dimensional spaces (46G05) Differentiable maps on manifolds (58C25) Implicit function theorems; global Newton methods on manifolds (58C15)

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Cites Work

• The implicit function theorem for ultradifferentiable mappings
• New proofs and generalizations of two theorems by Lednev for Goursat problems
• Non-linear leray-volevich systems and gevrey class
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