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

作者:Vesely Libor*; Zajicek Ludek
来源:Journal of Mathematical Analysis and Applications, 2018, 463(1): 167-175.
DOI:10.1016/j.jmaa.2018.03.021

摘要

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.

  • 出版日期2018-7-1

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