Real Analysis Exchange

The Implicit and Inverse Function Theorems: Easy Proofs

Oswaldo de Oliveira

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Abstract

This article presents simple and easy proofs of the Implicit Function Theorem and the Inverse Function Theorem, in this order, both of them on a finite-dimensional Euclidean space, that employ only the Intermediate-Value Theorem and the Mean-Value Theorem. These proofs avoid compactness arguments, the contraction principle, and fixed-point theorems.

Article information

Source
Real Anal. Exchange, Volume 39, Number 1 (2013), 207-218.

Dates
First available in Project Euclid: 1 July 2014

Permanent link to this document
https://projecteuclid.org/euclid.rae/1404230147

Mathematical Reviews number (MathSciNet)
MR3261906

Zentralblatt MATH identifier
1296.15014

Subjects
Primary: 26B10: Implicit function theorems, Jacobians, transformations with several variables 26B12: Calculus of vector functions
Secondary: 97140

Keywords
Implicit Function Theorems Calculus of Vector Functions Differential Calculus Functions of Several Variables

Citation

de Oliveira, Oswaldo. The Implicit and Inverse Function Theorems: Easy Proofs. Real Anal. Exchange 39 (2013), no. 1, 207--218. https://projecteuclid.org/euclid.rae/1404230147


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