Volume 23, Number 4, October-December 2017
|Page(s)||1617 - 1648|
|Published online||21 September 2017|
Notes on the trace problem for separately convex functions∗
Charles University, Faculty of Mathematics and Physics, Sokolovská 83, 186 75 Praha 8, Czech Republic.
Received: 9 September 2014
Revised: 7 September 2016
Accepted: 23 September 2016
We discuss the following question: for a function f of two or more variables which is convex in the directions of coordinate axes, what can its trace g(x) = f(x,x,...,x) look like? In the two-dimensional case, we provide some necessary and sufficient conditions, as well as some examples illustrating that our approach does not seem to be appropriate for finding a characterization in full generality. For a concave function g, however, a characterization in the two-dimensional case is established.
Mathematics Subject Classification: 26B25
Key words: Separately convex function / trace problem
© EDP Sciences, SMAI 2017
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