Data di Pubblicazione:
2018
Citazione:
A non-DC function which is DC along all convex curves / L. Vesely, L. Zajicek. - In: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. - ISSN 0022-247X. - 463:1(2018), pp. 167-175. [10.1016/j.jmaa.2018.03.021]
Abstract:
A problem asked by the authors in 1989 concerns the natural question, whether one can deduce that a continuous function f on an open convex set D subset of R-n is DC (i.e., is a difference of two convex functions) from the behavior of f "along some special curves phi". I.M. Prudnikov published in 2014 a theorem (working with convex curves phi in the plane), which would give a positive answer in R-2 to our problem. However, in the present note we construct an example showing that this theorem is not correct, and thus our problem remains open in each R-n, n > 1.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
DC function; d.c. function; Characterization of DC functions
Elenco autori:
L. Vesely, L. Zajicek
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