Lipschitz-like property of an implicit multifunction and its applications

2011 ◽  
Vol 74 (17) ◽  
pp. 6256-6264 ◽  
Author(s):  
Thai Doan Chuong
Keyword(s):  
Implicit Multifunction

On Implicit Multifunction Theorems

2008 ◽  
Vol 16 (2-3) ◽  
pp. 129-155 ◽  
Author(s):  
D. Azé ◽  
S. Benahmed
Keyword(s):  
Implicit Multifunction ◽  
Implicit Multifunction Theorems

scholarly journals Implicit multifunction theorems in complete metric spaces

2013 ◽  
Vol 139 (1-2) ◽  
pp. 301-326 ◽  
Author(s):  
van Ngai Huynh ◽  
Huu Tron Nguyen ◽  
Michel Théra
Keyword(s):  
Metric Spaces ◽  
Complete Metric Spaces ◽  
Implicit Multifunction ◽  
Implicit Multifunction Theorems

scholarly journals Implicit Multifunction Theorems in Banach Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Ming-ge Yang ◽  
Yi-fan Xu
Keyword(s):  
Variational Principle ◽  
Banach Spaces ◽  
Lower Semicontinuity ◽  
Metric Regularity ◽  
Sufficient Conditions ◽  
Clarke Subdifferential ◽  
Ekeland Variational Principle ◽  
Implicit Multifunction ◽  
Implicit Multifunction Theorems ◽  
The Clarke Subdifferential

This paper is mainly devoted to the study of implicit multifunction theorems in terms of Clarke coderivative in general Banach spaces. We present new sufficient conditions for the local metric regularity, metric regularity, Lipschitz-like property, nonemptiness, and lower semicontinuity of implicit multifunctions in general Banach spaces. The basic tools of our analysis involve the Ekeland variational principle, the Clarke subdifferential, and the Clarke coderivative.

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