Relationships between Robinson metric regularity and Lipschitz-like behavior of implicit multifunctions

By constructing some suitable examples, Jeyakumar and Yen (2004)  [1] have shown that the Robinson metric regularity (Rmr) and the Lipschitz-like property (Llp) of implicit multifunctions are not equivalent. This paper clarifies relationships between the two properties of implicit multifunctions. It...

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Vydáno v:Nonlinear analysis Ročník 72; číslo 9; s. 3594 - 3601
Hlavní autoři: Chieu, N.H., Yao, J.-C., Yen, N.D.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Amsterdam Elsevier Ltd 01.05.2010
Elsevier
Témata:
Construction
Equivalence
Exact sciences and technology
Implicit multifunction
Lipschitz-like property
Mathematical analysis
Mathematics
Nonlinearity
Normal coderivative
Regularity
Relationship
Robinson metric regularity
Sciences and techniques of general use
Theorems
secondary
Lipschitz-like property
Robinson metric regularity
Normal coderivative
Relationship
Implicit multifunction
primary
Nonlinear analysis
Mathematical model
primary 49J53
47H04
secondary 54C60
ISSN:0362-546X, 1873-5215
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Shrnutí:By constructing some suitable examples, Jeyakumar and Yen (2004)  [1] have shown that the Robinson metric regularity (Rmr) and the Lipschitz-like property (Llp) of implicit multifunctions are not equivalent. This paper clarifies relationships between the two properties of implicit multifunctions. It turns out that the (reasonable) sufficient conditions for having (Rmr) ⇒ (Llp) are quite different from those for the validity of the reverse implication. The implicit function theorem due to Yen and Yao (2009) [2] serves as a tool for our analysis of (Rmr) and (Llp).
Bibliografie:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
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ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2009.12.039