Rolle's theorem and negligibility of points in infinite dimensional Banach spaces

DOI10.1006/jmaa.1997.5552zbMath0897.46027OpenAlexW1995002294MaRDI QIDQ1378709

J. Ning

Publication date: 19 October 1998

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

Full work available at URL: https://semanticscholar.org/paper/16c417ec866de4e4d58a9481ef733089c1b8117d

zbMATH Keywords

Rolle's theorem in infinite-dimensional Banach spaces\(C^1\) bump functionapproximate Rolle's theoremcontinuous norm whose dual norm is locally uniformly rotund

Mathematics Subject Classification ID

Geometry and structure of normed linear spaces (46B20) Isometric theory of Banach spaces (46B04) Derivatives of functions in infinite-dimensional spaces (46G05)

Related Items (8)

Approximate Rolle's theorems for the proximal subgradient and the generalized gradient. ⋮ Ulam Stability of Zero Point Equations ⋮ Lineability, differentiable functions and special derivatives ⋮ James' theorem fails for starlike bodies ⋮ The failure of Rolle's theorem in infinite-dimensional Banach spaces ⋮ Nonsmooth analysis and Hamilton--Jacobi equations on Riemannian manifolds ⋮ Rolle's theorem for polynomials of degree four in a Hilbert space. ⋮ An approximate Rolle's theorem for polynomials of degree four in a Hilbert space

Cites Work

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• Convex functions, monotone operators and differentiability.
• On Rolle's theorem in infinite-dimensional Banach spaces
• On smooth variational principles in Banach spaces
• Smooth and R-analytic negligibility of subsets and extension of homeomorphisms in Banach spaces
• Nonconvex minimization problems
• Rolle's Theorem Fails in l 2

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