  The univariate spline quasi-interpolants (abbr. QIs) studied in this paper
are approximation operators using B-spline expansions with coefficients which
are linear combinations of discrete or weighted mean values of the function to
be approximated. When working with nonuniform partitions, the main challenge is
to find QIs which have both good approximation orders and uniform norms which
are bounded independently of the given partition. Near-best QIs are obtained by
minimizing an upper bound of the infinity norm of QIs depending on a certain
number of free parameters, thus reducing this norm. This paper is devoted to
the study of two families of near-best QIs of approximation order 3.
