Geodesic
The distance between subdifferentials in the terms of functions
Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993) no. 3, pp. 419-424 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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For convex continuous functions $f,g$ defined respectively in neighborhoods of points $x,y$ in a normed linear space, a formula for the distance between $\partial f(x)$ and $\partial g(y)$ in terms of $f,g$ (i.e\. without using the dual) is proved. Some corollaries, like a new characterization of the subdifferential of a continuous convex function at a point, are given. This, together with a theorem from [4], implies a sufficient condition for a family of continuous convex functions on a barrelled normed linear space to be locally uniformly Lipschitz.
For convex continuous functions $f,g$ defined respectively in neighborhoods of points $x,y$ in a normed linear space, a formula for the distance between $\partial f(x)$ and $\partial g(y)$ in terms of $f,g$ (i.e\. without using the dual) is proved. Some corollaries, like a new characterization of the subdifferential of a continuous convex function at a point, are given. This, together with a theorem from [4], implies a sufficient condition for a family of continuous convex functions on a barrelled normed linear space to be locally uniformly Lipschitz.
Classification : 26B25, 46A08, 46N10, 49J52, 52A41
Keywords: convex analysis; subdifferentials of convex functions; barrelled normed linear spaces 
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     title = {The distance between subdifferentials in the terms of functions},
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Veselý, Libor. The distance between subdifferentials in the terms of functions. Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993) no. 3, pp. 419-424. http://geodesic.mathdoc.fr/item/CMUC_1993_34_3_a3/