Geodesic
Some remarks on the space of differences of sublinear functions
Applicationes Mathematicae, Tome 22 (1993) no. 3, pp. 419-426 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 conjugate of the farthest point mapping to its subdifferential at the origin. This leads to a simple family of sublinear functions which contains an exhaustive family of upper convex approximations for any quasidifferentiable function.
DOI : 10.4064/am-22-3-419-426
Keywords: upper convex approximation, sublinear function, Fenchel conjugation, quasidifferentiable function

Sven Bartels 1 ; Diethard Pallaschke 1

1 
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Sven Bartels; Diethard Pallaschke. Some remarks on the space of differences of sublinear functions. Applicationes Mathematicae, Tome 22 (1993) no. 3, pp. 419-426. doi: 10.4064/am-22-3-419-426

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