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A $C^1$ function even on the sphere with no critical point in the ball

Borwein, Jonathan M. and Kortezov, Ivaylo and Wiersma, Herre (2002) A $C^1$ function even on the sphere with no critical point in the ball. International J. Nonlinear and Convex Analysis, 3 . pp. 1-16.

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      Abstract

      In this article we construct a real-valued $C^1$-function on the closed ball in $\R^2$ that is even on the boundary of the ball, and has no critical points inside the ball. This provides a counterexample to a nonsmooth Rolle-type theorem sought in \cite{BF}.

      Item Type: Article
      Additional Information: pubdom FALSE
      Uncontrolled Keywords: Rolle's theorem, mean value inequalities, duality inequalities, nonsmooth analysis, Clarke subdifferential
      Subjects: 46-xx Functional analysis
      Faculty: UNSPECIFIED
      Depositing User: Users 1 not found.
      Date Deposited: 24 Nov 2003
      Last Modified: 13 Jan 2015 11:55
      URI: https://docserver.carma.newcastle.edu.au/id/eprint/140

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