Abstract :
In this paper, we use a probabilistic setting to introduce a double sequence
ŽL²nk: . of linear polynomial operators which includes, as particular cases, the
classical Bernstein operators, the Kantoroviˇc operators, and the operators recently
introduced by Cao. For these operators, we discuss several approximation properties.
In particular, we deal with the convergence properties according to the way in
which the different parameters vary, and the preservation of global smoothness and
classes of functions determined by concave moduli of continuity. A remarkable
feature of our approach is that if f is differentiable, the approximation properties
of both L²nk: f and its derivatives can be discussed simultaneously. Throughout the
paper, probabilistic methods play an important role.
