Abstract:
This paper deals with the modified
$q$-Stancu–Beta operators
and investigates statistical
approximation theorems for these operators with the
help of a Korovkin-type approximation theorem.
The rates of statistical
convergence are determined by means of the modulus of continuity
and a Lipschitz-type maximal function.
The results show that
the rates of convergence of
the operators under consideration are at least as fast as those of
the classical Stancu–Beta operators.
Keywords:$q$-integers, statistical convergence,
$q$-Stancu–Beta
operators, rate of statistical convergence, modulus of
continuity, positive linear operators, Korovkin-type approximation theorem.
