Compactly epi-Lipschitzian convex sets and functions in normed spaces.
Borwein, Jonathan, Lucet, Yves, Mordukhovich, Boris (2000)
Journal of Convex Analysis
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Borwein, Jonathan, Lucet, Yves, Mordukhovich, Boris (2000)
Journal of Convex Analysis
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Kragujevac Journal of Mathematics
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Two properties concerning the space of differences of sublinear functions D(X) for a real Banach space X are proved. First, we show that for a real separable Banach space (X,‖·‖) there exists a countable family of seminorms such that D(X) becomes a Fréchet space. For X = ℝ^n this construction yields a norm such that D(ℝ^n) becomes a Banach space. Furthermore, we show that for a real Banach space with a smooth dual every sublinear Lipschitzian function can be expressed by the Fenchel...
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