On a theorem of Lyusternik
type: Item
instance of: scholarly article
title: On a theorem of Lyusternik
zbMATH Open document ID: 0581.46035
DOI: 10.1016/0022-247X(85)90346-4
author: Chung-Wei Ha
published in: Journal of Mathematical Analysis and Applications
publication date: 1985-01-01T00:00:00Z
review text: We propose a new proof of the following Lyusternik's theorem. Let E,F be Banach spaces, \(X\subset E\) be an open set and let \(x_ 0\in X\). If \(f: X\to F\) is a map strictly differentiable at \(x_ 0\) and if the differential \(Df(x_ 0)\) of f at \(x_ 0\) maps E onto F, then there exists a constant \(M>0\) and a neighborhood U of \(x_ 0\) in X such that \(dist(x,\Omega)\leq M\| f(x)- f(x_ 0)\|\) for all \(x\in U\), where \(\Omega =\{y\in X:\quad f(y)=f(x_ 0)\}.\)
Mathematics Subject Classification ID: 46G05
zbMATH DE Number: 3929711
zbMATH Keywords: Lyusternik's theorem
zbMATH Keywords: strictly differentiable
MaRDI profile type: Publication
cites work: LYUSTERNIK'S THEOREM AND THE THEORY OF EXTREMA
cites work: Extremum problems in the presence of restrictions
cites work: Lectures on mathematical theory of extremum problems. Translated from the Russian by D. Louvish
cites work: Q4194725
cites work: Q3274351
description: scientific article; zbMATH DE number 3929711