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On Rolle's theorem in infinite-dimensional Banach spaces

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Publication:1311108
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DOI10.1007/BF01206400zbMath0786.46044OpenAlexW2020332034MaRDI QIDQ1311108

Stanislav Shkarin

Publication date: 8 February 1994

Published in: Mathematical Notes (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01206400


zbMATH Keywords

Rolle's theorem in infinite-dimensional Banach spaces


Mathematics Subject Classification ID

Derivatives of functions in infinite-dimensional spaces (46G05)


Related Items (9)

Approximation by smooth functions with no critical points on separable Banach spaces ⋮ Rolle's theorem and negligibility of points in infinite dimensional Banach spaces ⋮ Approximate Rolle's theorems for the proximal subgradient and the generalized gradient. ⋮ Lineability, differentiable functions and special derivatives ⋮ A note on the range of the derivatives of analytic approximations of uniformly continuous functions on \(c_0\) ⋮ James' theorem fails for starlike bodies ⋮ The failure of Rolle's theorem in infinite-dimensional Banach spaces ⋮ 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



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