A non-DC function which is DC along all convex curves

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F18%3A10390808" target="_blank" >RIV/00216208:11320/18:10390808 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1016/j.jmaa.2018.03.021" target="_blank" >https://doi.org/10.1016/j.jmaa.2018.03.021</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jmaa.2018.03.021" target="_blank" >10.1016/j.jmaa.2018.03.021</a>

Result language
angličtina
Original language name
A non-DC function which is DC along all convex curves
Original language description
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.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA15-08218S" target="_blank" >GA15-08218S: Theory of real functions and its applications in geometry</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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