ISSN:
1572-932X
Keywords:
nonsmooth analysis
;
subdifferentials
;
coderivatives
;
implicit function theorem
;
solvability
;
stability
;
open mapping theorem
;
metric regularity
;
multidirectional mean value inequality
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract We prove a general implicit function theorem for multifunctions with a metric estimate on the implicit multifunction and a characterization of its coderivative. Traditional open covering theorems, stability results, and sufficient conditions for a multifunction to be metrically regular or pseudo-Lipschitzian can be deduced from this implicit function theorem. We prove this implicit multifunction theorem by reducing it to an implicit function/solvability theorem for functions. This approach can also be used to prove the Robinson–Ursescu open mapping theorem. As a tool for this alternative proof of the Robinson–Ursescu theorem, we also establish a refined version of the multidirectional mean value inequality which is of independent interest.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1008775413250
