An implicit function theorem for one-sided Lipschitz mappings
type: Item
instance of: scholarly article
title: An implicit function theorem for one-sided Lipschitz mappings
zbMATH Open document ID: 1235.47056
author: Wolf-Jürgen Beyn
author: Janosch Rieger
published in: Set-Valued and Variational Analysis
publication date: 2011-11-08T00:00:00Z
review text: Using a local existence theorem for the solution of a zero-point inclusion \[ 0\in F(x),\;x\in \mathbb{R}^m, \] the authors obtain both local and global implicit function theorems for set-valued equations with relaxed one-sided Lipschitz set-valued operators \(F:\mathbb{R}^k\times \mathbb{R}^m\to P_{cp,cv}(\mathbb{R}^m)\). Finally, as an application, Crank-Nicolson schemes for differential inclusions and differential algebraic inclusions are given.
reviewed by: Adrian Petruşel
Mathematics Subject Classification ID: 47J07
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 47N20
Mathematics Subject Classification ID: 34A60
zbMATH DE Number: 5969027
zbMATH Keywords: set-valued implicit function theorem
zbMATH Keywords: one-sided Lipschitz condition
zbMATH Keywords: differential (algebraic) inclusions
MaRDI profile type: Publication
full work available at URL: s11228-010-0162-8
OpenAlex ID: W2073279297
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DOI: 10.1007/S11228-010-0162-8
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description: scientific article; zbMATH DE number 5969027