An open mapping principle for set-valued maps

DOI10.1016/0022-247X(87)90149-1zbMath0643.46034MaRDI QIDQ1101928

Hélène Frankowska

Publication date: 1987

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

zbMATH Keywords

set-valued maphigh-order open mapping principle

Mathematics Subject Classification ID

Set-valued functions (26E25) Derivatives of functions in infinite-dimensional spaces (46G05)

Related Items (34)

On higher-order adjacent derivative of perturbation map in parametric vector optimization ⋮ Variations of a control process at the initial point ⋮ Metric regularity and second-order necessary optimality conditions for minimization problems under inclusion constraints ⋮ Implicit function theorems for nondifferentiable mappings ⋮ A high-order generalization of the Lyusternik theorem ⋮ Conical inverse mapping theorems ⋮ Local controllability of control systems with feedback ⋮ Equi-surjective systems of linear operators and applications ⋮ An Induction Theorem and Nonlinear Regularity Models ⋮ Inverse and implicit function theorems for nonsmooth maps in Banach spaces ⋮ Inclusions in general spaces: Hoelder stability, solution schemes and Ekeland's principle ⋮ Verifiable necessary and sufficient conditions for openness and regularity of set-valued and single-valued maps ⋮ Lipschitzian stability of constraint systems and generalized equations ⋮ Nonlinear regularity models ⋮ On higher-order proto-differentiability of perturbation maps ⋮ On metric regularity of multifunctions ⋮ Hölder metric regularity of set-valued maps ⋮ Small-time local controllability of the bilinear Schrödinger equation with a nonlinear competition ⋮ Error bounds and Hölder metric subregularity ⋮ Metric subregularity of order \(q\) and the solving of inclusions ⋮ A Hamiltonian approach to small time local attainability of manifolds for nonlinear control systems ⋮ High order inverse function theorems ⋮ On mappings covering at a nonlinear rate and their perturbation stability ⋮ High-order tangent cones and their application in optimization ⋮ Nonlinear metric subregularity ⋮ Complete Characterization of Openness, Metric Regularity, and Lipschitzian Properties of Multifunctions ⋮ Covering properties at positive-order rates of multifunctions and some related topics ⋮ Verifiable Conditions for Openness and Regularity of Multivalued Mappings in Banach Spaces ⋮ Transversality properties: primal sufficient conditions ⋮ Multivalued Functions Integration: from Additive to Arbitrary Non-negative Set Function ⋮ On Small-Time Local Controllability ⋮ Subtraction theorems and approximate openness for multifunctions: Topological and infinitesimal viewpoints ⋮ Stable approximations of set-valued maps ⋮ Some inverse mapping theorems

Cites Work

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• Local controllability of control systems with feedback
• On inverse function theorems for set-valued maps
• Interior mapping theorem with set-valued derivatives
• On the variational principle
• On the inversion of some differentiable mappings with singularities between Banach spaces
• Extensions of subgradient calculus with applications to optimization
• Higher Order Conditions with and without Lagrange Multipliers
• On the local surjection property
• An Implicit Function Theorem for Nondifferentiable Mappings

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