A general metric regularity in asplund banach spaces

1998 ◽  
Vol 19 (3-4) ◽  
pp. 215-226 ◽  
Author(s):  
T. Amahroq ◽  
A. Jourani ◽  
L. Thibault
Keyword(s):  
Banach Spaces ◽  
Metric Regularity

scholarly journals METRIC REGULARITY OF COMPOSITE MULTIFUNCTIONS IN BANACH SPACES

2009 ◽  
Vol 13 (6A) ◽  
pp. 1723-1735 ◽  
Author(s):  
Xi Yin Zheng ◽  
Kung Fu Ng
Keyword(s):  
Banach Spaces ◽  
Metric Regularity

scholarly journals Restrictive metric regularity and generalized differential calculus in Banach spaces

2004 ◽  
Vol 2004 (50) ◽  
pp. 2653-2680 ◽  
Author(s):  
Boris S. Mordukhovich ◽  
Bingwu Wang
Keyword(s):  
Banach Spaces ◽  
Differential Calculus ◽  
Metric Regularity ◽  
Sufficient Conditions ◽  
Normal Cones ◽  
First Order ◽  
Nonconvex Sets ◽  
Generalized Differential ◽  
Necessary And Sufficient ◽  
Generalized Differential Calculus

We consider nonlinear mappingsf:X→Ybetween Banach spaces and study the notion ofrestrictive metric regularityoffaround some pointx¯, that is, metric regularity offfromXinto the metric spaceE=f(X). Some sufficient as well as necessary and sufficient conditions for restrictive metric regularity are obtained, which particularly include an extension of the classical Lyusternik-Graves theorem in the case whenfis strictly differentiable atx¯but its strict derivative∇f(x¯)is not surjective. We develop applications of the results obtained and some other techniques in variational analysis to generalized differential calculus involving normal cones to nonsmooth and nonconvex sets, coderivatives of set-valued mappings, as well as first-order and second-order subdifferentials of extended real-valued functions.

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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