Remarks on the inverse and implicit function theorems for differentiable functions

DOI10.1007/s40590-021-00327-1zbMath1465.58006OpenAlexW3129229278MaRDI QIDQ2024024

Marcio Colombo Fenille, Telmo Irineo Acosta Vellozo

Publication date: 3 May 2021

Published in: Boletín de la Sociedad Matemática Mexicana. Third Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40590-021-00327-1

zbMATH Keywords

implicit function theoreminverse function theoremdegree of a functionexistence and uniqueness theorem for ordinary differential equations

Mathematics Subject Classification ID

Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations (34A12) Degree, winding number (55M25) Differentiable maps on manifolds (58C25) Implicit function theorems; global Newton methods on manifolds (58C15)

Related Items (2)

New inverse and implicit function theorems for differentiable maps with isolated critical points ⋮ Differentiable maps with isolated critical points are not necessarily open in infinite dimensional spaces

Cites Work

• Inverse mapping theorem and local forms of continuous mappings
• The implicit function theorem for continuous functions
• Local inversion theorems without assuming continuous differentiability
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