  The constrained mock-Chebyshev least squares operator is a linear
approximation operator based on an equispaced grid of points. Like other
polynomial or rational approximation methods, it was recently introduced in
order to defeat the Runge phenomenon that occurs when using polynomial
interpolation on large sets of equally spaced points. The idea is to improve
the mock-Chebyshev subset interpolation, where the considered function $f$ is
interpolated only on a proper subset of the uniform grid, formed by nodes that
mimic the behavior of Chebyshev--Lobatto nodes. In the mock-Chebyshev subset
interpolation all remaining nodes are discarded, while in the constrained
mock-Chebyshev least squares interpolation they are used in a simultaneous
regression, with the aim to further improving the accuracy of the approximation
provided by the mock-Chebyshev subset interpolation. The goal of this paper is
two-fold. We discuss some theoretical aspects of the constrained mock-Chebyshev
least squares operator and present new results. In particular, we introduce
explicit representations of the error and its derivatives. Moreover, for a
sufficiently smooth function $f$ in $[-1,1]$, we present a method for
approximating the successive derivatives of $f$ at a point $x\in [-1,1]$, based
on the constrained mock-Chebyshev least squares operator and provide estimates
for these approximations. Numerical tests demonstrate the effectiveness of the
proposed method.
