On the existence of zero points
type: Item
instance of: scholarly article
title: On the existence of zero points
zbMATH Open document ID: 0859.65049
DOI: 10.1016/0096-3003(95)00246-4
author: Yanyan Li
published in: Applied Mathematics and Computation
publication date: 1996-10-07T00:00:00Z
review text: The author proves that a continuous function \(F:\mathbb{R}^n\to\mathbb{R}^n\) has at least one zero under one of two smoothness conditions. The constructive proof, based on a homotopy, uses the implicit function theorem and contains a proof of a global implicit function theorem. Numerical methods can be used to follow a solution curve, though no numerical examples are given.
Mathematics Subject Classification ID: 65H10
Mathematics Subject Classification ID: 26B05
Mathematics Subject Classification ID: 26B10
zbMATH DE Number: 932158
zbMATH Keywords: zeros of continuous multivariate functions
zbMATH Keywords: implicit function theorem
zbMATH Keywords: solution curve
reviewed by: Adrian Swift
MaRDI profile type: Publication
full work available at URL: 0096-3003(95)00246-4
OpenAlex ID: W2078379671
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description: scientific article; zbMATH DE number 932158