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.
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.
|Titolo:||A non-DC function which is DC along all convex curves|
VESELY, LIBOR (Corresponding)
|Parole Chiave:||DC function; d.c. function; Characterization of DC functions|
|Settore Scientifico Disciplinare:||Settore MAT/05 - Analisi Matematica|
|Data di pubblicazione:||2018|
|Digital Object Identifier (DOI):||http://dx.doi.org/10.1016/j.jmaa.2018.03.021|
|Appare nelle tipologie:||01 - Articolo su periodico|