The L p -saturation for linear combination of Bernstein-Kantorovich operators

Abstract

We study the L p -saturation for the linear combination of BernsteinKantorovich operators. As a result we obtain the saturation class by using K-functional as well as some modulus of smoothness.

On Certain Properties of the Combinations of Szász-Durrmeyer Operators

“…It is a generalization of combination defined by P. L. Butzer. For the other types operators similar definitions can be found in [4,9]. As it was mentioned before we use the ideas introduced by M. Heilmann [6] , and later applied by D. Zhou [6] and Guo S., Li C., Sun Y., Yang G., Yue S [8] .…”

The lower estimate for the linear combinations of Bernstein–Kantorovich operators

“…However, the saturation problem for all r ≥ 1 was first solved in [5]. Some notations are necessary to be mentioned.…”

“…In [5] we studied also the problem that one can replace K ( f, r, t) p = O(t 2r ) by ω 2r ϕ ( f, t) p = O(t 2r ). We have (see [5]).…”