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Remarks on delta-convex functions. (English) Zbl 0714.46007
Let A be a convex subset of a normed linear space X. A function H: \(A\to {\mathbb{R}}\) is delta-convex on A if it can be expressed as a difference of two continuous convex functions on A. A function h: \(A\to {\mathbb{R}}\) is a control function to H on A if h-H and \(h+H\) are continuous and convex.
The authors give an example of a delta-convex function on \({\mathbb{R}}^ 2\) which is strictly differentiable at 0, but none of its control functions is differentiable at 0. They also generalize to infinite-dimensional spaces a result of Hartman on the existence of a control function for a family of functions.
Reviewer: V.Anisiu

46A55 Convex sets in topological linear spaces; Choquet theory
26B25 Convexity of real functions of several variables, generalizations
46G05 Derivatives of functions in infinite-dimensional spaces
49J50 Fréchet and Gateaux differentiability in optimization
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