  Using two results of Garkavi, Medvedev and Khavinson, we give sufficient
conditions for proximinality of sums of two ridge functions with bounded and
continuous summands in the spaces of bounded and continuous multivariate
functions respectively. In the first case, we give an example which shows that
the corresponding sufficient condition cannot be made weaker for some subsets
of $\mathbb{R}^{n}$. In the second case, we obtain also a necessary condition
for proximinality. All the results are furnished with plenty of examples. The
results, examples and following discussions naturally lead us to a conjecture
on the proximinality of the considered class of ridge functions. The main
purpose of the paper is to draw readers' attention to this conjecture.
