Remarks on the inverse and implicit function theorems for differentiable functions

We propose a detailed description for the proofs of the key results that support the inverse function theorem for differentiable functions (presented by Radulescu and Radulescu in J Math Anal Appl 138(2):581–590, 1989), an extension for one of that results for continuous functions and a complete pro...

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Bibliographic Details
Published in:Boletín de la Sociedad Matemática Mexicana Vol. 27; no. 1
Main Authors: Fenille, Marcio Colombo, Vellozo, Telmo Irineo Acosta
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 01.03.2021
Springer Nature B.V
Subjects:
Boundary value problems
Continuity (mathematics)
Existence theorems
Mathematics
Mathematics and Statistics
Original Article
Uniqueness theorems
58C15
55M25
Inverse function theorem
58C25
34A12
Existence and uniqueness theorem for ordinary differential equations
Implicit function theorem
Degree of a function
ISSN:1405-213X, 2296-4495
Online Access:Get full text
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Summary:We propose a detailed description for the proofs of the key results that support the inverse function theorem for differentiable functions (presented by Radulescu and Radulescu in J Math Anal Appl 138(2):581–590, 1989), an extension for one of that results for continuous functions and a complete proof for that version of the inverse function theorem itself. Furthermore, by means of a technical strengthening of the hypothesis, we transmute an existence theorem for certain initial value problems, proposed by Biasi et al. (Topol Methods Nonlinear Anal 32(1), 177–186, 2008), to a uniqueness and existence theorem.
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ISSN:1405-213X
2296-4495
DOI:10.1007/s40590-021-00327-1