Publication at Faculty of Mathematics and Physics |
2017
Abstract
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.