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 |
Autori: | |
Parole Chiave: | DC function; d.c. function; Characterization of DC functions |
Settore Scientifico Disciplinare: | Settore MAT/05 - Analisi Matematica |
Data di pubblicazione: | 2018 |
Rivista: | |
Tipologia: | Article (author) |
Digital Object Identifier (DOI): | http://dx.doi.org/10.1016/j.jmaa.2018.03.021 |
Appare nelle tipologie: | 01 - Articolo su periodico |
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