an:04175726
Zbl 0714.46007
Kopeck??, Eva; Mal??, Jan
Remarks on delta-convex functions
EN
Commentat. Math. Univ. Carol. 31, No. 3, 501-510 (1990).
00156064
1990
j
46A55 26B25 46G05 49J50
control function; delta-convex function; strictly differentiable
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.
V.Anisiu