On Kantorovich-type operator.
It is shown that a Korovkin type theorem for a sequence of linear positive operators acting in weighted space does not hold in all this space and is satisfied only on some subspace.
This paper is motivated by Kirov results on generalized Bernstein polynomials given in (Kirov, G. H., A generalization of the Bernstein polynomials, Math. Balk. New Ser. bf 6 (1992), 147–153.). We introduce certain modified Meyer-König and Zeller operators in the space of differentiable functions of two variables and we study approximation properties for them. Some approximation properties of the Meyer-König and Zeller operators of differentiable functions of one variable are given in (Rempulska,...
The present paper shows that for any sequences of real numbers, each with infinitely many distinct elements, , j=1,...,s, the rational combinations of are always dense in .