Mappings sharing a value on finite-dimensional spaces
type: Item
instance of: scholarly article
title: Mappings sharing a value on finite-dimensional spaces
zbMATH Open document ID: 1028.58009
DOI: 10.1016/S0096-3003(00)00023-0
author: Yanyan Li
published in: Applied Mathematics and Computation
publication date: 2003-01-28T00:00:00Z
review text: Let \(f\) and \(g\) be \(C^1\) maps between \(\mathbb{R}^n\) and \(\mathbb{R}^m\) with \(m\leq n\). Assuming that \(f\) is proper and has at least one zero, the author states a sufficient condition ensuring that the map \(f-g\) also has a zero. The proof is based on elementary arguments, but it is obscured by the careless writing (a sample of which is given by ``the product of Banach spaces \([0,1]\times X_1\) and \(X_2\)'' on page 394). It also seems that the statement of assumption (iii) should involve ``\(f(x)\neq tg(x)\)'' instead of ``\(f(x)\neq g(x)\)''.
Mathematics Subject Classification ID: 58C25
Mathematics Subject Classification ID: 26B10
zbMATH DE Number: 1860900
zbMATH Keywords: zeros of mappings
zbMATH Keywords: implicit function theorem
zbMATH Keywords: homotopy methods
reviewed by: Vincent Thilliez
MaRDI profile type: Publication
cites work: Global minimum point of a convex function
cites work: Extremum points of a convex function
cites work: On the existence of zero points
cites work: On the number of zeros of a mapping
cites work: Existence of zeros for bounded perturbations of proper mappings
cites work: Q3998344
cites work: The Homotopy Continuation Method: Numerically Implementable Topological Procedures
cites work: Q3949869
cites work: Computing Kakutani Fixed Points
cites work: On the Number of Solutions to Polynomial Systems of Equations
cites work: Determining All Solutions to Certain Systems of Nonlinear Equations
cites work: Q3657778
cites work: Q4342526
cites work: Q3706043
cites work: Q3479457
cites work: A special type of triangulations in numerical nonlinear analysis
cites work: Q3795617
cites work: Applied functional analysis. Main principles and their applications
description: scientific article; zbMATH DE number 1860900