Smooth approximations without critical points

DOI10.2478/BF02475210zbMath1033.46037OpenAlexW2047150521MaRDI QIDQ1407192

Michal Johanis, Petr Hájek

Publication date: 2003

Published in: Central European Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2478/bf02475210

zbMATH Keywords

critical pointsderivativesapproximation by smooth functions

Mathematics Subject Classification ID

Geometry and structure of normed linear spaces (46B20) Derivatives of functions in infinite-dimensional spaces (46G05)

Related Items (4)

Approximation by smooth functions with no critical points on separable Banach spaces ⋮ A note on the range of the derivatives of analytic approximations of uniformly continuous functions on \(c_0\) ⋮ Extraction of critical points of smooth functions on Banach spaces ⋮ Smooth approximations without critical points of continuous mappings between Banach spaces, and diffeomorphic extractions of sets

Cites Work

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• Norms with locally Lipschitzian derivatives
• Optimization of functions on certain subsets of Banach spaces
• Smooth functions on \(c_0\)
• The range of the gradient of a Lipschitz \(C^1\)-smooth bump in infinite dimensions
• Uniform approximation of continuous mappings by smooth mappings with no critical points on Hilbert manifolds
• Exact Filling of Figures with the Derivatives of Smooth Mappings Between Banach Spaces
• On the range of the derivatives of a smooth function between Banach spaces
• On the range of the derivative of a real-valued function with bounded support
• Filling analytic sets by the derivatives of 𝐶¹-smooth bumps
• James' theorem fails for starlike bodies
• The failure of Rolle's theorem in infinite-dimensional Banach spaces

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