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- W68084328 abstract "Given a convex set $C$ in a real vector space $E$ and two points $x,yin C$, we investivate which are the possible values for the variation $f(y)-f(x)$, where $f:Clongrightarrow [m,M]$ is a bounded convex function. We then rewrite the bounds in terms of the Funk weak metric, which will imply that a bounded convex function is Lipschitz-continuous with respect to the Thompson and Hilbert metrics. The bounds are also proved to be optimal. We also exhibit the maximal subdifferential of a bounded convex function at a given point $xin C$." @default.
- W68084328 created "2016-06-24" @default.
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- W68084328 date "2017-01-01" @default.
- W68084328 modified "2023-10-17" @default.
- W68084328 title "A universal bound on the variations of bounded convex functions" @default.
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- W68084328 hasPublicationYear "2017" @default.
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