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2013/2014 The Implicit and Inverse Function Theorems: Easy Proofs
Oswaldo de Oliveira
Real Anal. Exchange 39(1): 207-218 (2013/2014).


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.


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Oswaldo de Oliveira. "The Implicit and Inverse Function Theorems: Easy Proofs." Real Anal. Exchange 39 (1) 207 - 218, 2013/2014.


Published: 2013/2014
First available in Project Euclid: 1 July 2014

zbMATH: 1296.15014
MathSciNet: MR3261906

Primary: 26B10 , 26B12
Secondary: 97140

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

Rights: Copyright © 2013 Michigan State University Press

Vol.39 • No. 1 • 2013/2014
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