An Implicit Function Theorem for One-sided Lipschitz Mappings

Implicit function theorems are derived for nonlinear set valued equations that satisfy a relaxed one-sided Lipschitz condition. We discuss a local and a global version and study in detail the continuity properties of the implicit set-valued function. Applications are provided to the Crank–Nicolson s...

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Bibliographic Details
Published in:Set-valued and variational analysis Vol. 19; no. 3; pp. 343 - 359
Main Authors: Beyn, Wolf-Jürgen, Rieger, Janosch
Format: Journal Article
Language:English
Published: Dordrecht Springer Netherlands 01.09.2011
Subjects:
Analysis
Mathematics
Mathematics and Statistics
Optimization
One-sided Lipschitz condition
Set valued implicit function theorem
47H10
34A60
Differential (algebraic) inclusions
47N20
ISSN:1877-0533, 1877-0541
Online Access:Get full text
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Summary:Implicit function theorems are derived for nonlinear set valued equations that satisfy a relaxed one-sided Lipschitz condition. We discuss a local and a global version and study in detail the continuity properties of the implicit set-valued function. Applications are provided to the Crank–Nicolson scheme for differential inclusions and to the analysis of differential algebraic inclusions.
ISSN:1877-0533
1877-0541
DOI:10.1007/s11228-010-0162-8