Lyusternik--Graves Theorems for the Sum of a Lipschitz Function and a Set-valued Mapping
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چکیده
منابع مشابه
Lyusternik-Graves Theorems for the Sum of a Lipschitz Function and a Set-valued Mapping
In a paper of 1950 Graves proved that for a function f acting between Banach spaces and an interior point x̄ in its domain, if there exists a continuous linear mapping A which is surjective and the Lipschitz modulus of the difference f −A at x̄ is sufficiently small, then f is (linearly) open at x̄. This is an extension of the Banach open mapping principle from continuous linear mappings to Lipsch...
متن کاملGraves-type Theorems for the Sum of a Lipschitz Function and a Set-valued Mapping
In a paper of 1950 L. M. Graves proved that, for a function f acting between Banach spaces and an interior point x̄ in its domain, if there exists a continuous linear mapping A which is surjective and the Lipschitz modulus of the difference f − A at x̄ is sufficiently small, then f is (linearly) open at x̄. This is an extension of the Banach open mapping principle from continuous linear mappings t...
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ژورنال
عنوان ژورنال: SIAM Journal on Control and Optimization
سال: 2016
ISSN: 0363-0129,1095-7138
DOI: 10.1137/16m1063150