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Constrained Open Mapping Theorems And Applications
Author(s) -
Bian W.,
Webb J. R. L.
Publication year - 1999
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/s0024610799008078
Subject(s) - mathematics , controllability , differentiable function , constraint (computer aided design) , lipschitz continuity , nonlinear system , regular polygon , variational principle , mathematical optimization , pure mathematics , mathematical analysis , geometry , physics , quantum mechanics
Some constrained open mapping theorems are obtained via Ekeland's variational principle. The constraint need only be a closed subset when the mapping is assumed to be Lipschitz, or a closed convex cone when the mapping is assumed to be closed. Generalizations of some previous results of Welsh and others are obtained. Apart from the presence of a constraint and a different method, the differentiability assumptions made are weaker. As applications, two results on the constrained controllability of nonlinear systems are given.