  We discuss the following question: For a function f of two or more variables
which is convex in the directions of coordinate axes, how 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.
