  We extend the work by Mastroianni and Szabados regarding the barycentric
interpolant introduced by J.-P. Berrut in 1988, for equally spaced nodes. We
prove fully their first conjecture and present a proof of a weaker version of
their second conjecture. More importantly than proving these conjectures, we
present a sharp description of the asymptotic error incurred by the
interpolants when the derivative of the interpolated function is absolutely
continuous, which is a class of functions broad enough to cover most functions
usually found in practice. We also contribute to the solution of the broad
problem they raised regarding the order of approximation of these interpolants,
by showing that they have order of approximation of order 1/n for functions
with derivatives of bounded variation.
