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Implicit multifunction theorems in Banach spaces. (English) Zbl 1406.49015
Summary: 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.
MSC:
49J53 Set-valued and variational analysis
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