Approximation by α-Bernstein-Schurer operator

Statistical approximation of modified Schurer-type q-Bernstein Kantorovich operators

New modified Schurer-type q-Bernstein Kantorovich operators are introduced. The local theorem and statistical Korovkin-type approximation properties of these operators are investigated. Furthermore, the rate of approximation is examined in terms of the modulus of continuity and the elements of Lipschitz class functions.

Modified (p,q)-Bernstein-Schurer operators and their approximation properties

Approximation of Schurer type q-Bernstein-Kantorovich operators

*Correspondence: [email protected] 1Department of Mathematics and Computer Science, Wuyi University, Wuyishan, 354300, China Full list of author information is available at the end of the article Abstract In this paper, a kind of Schurer type q-Bernstein-Kantorovich operators is introduced. The Korovkin type approximation theorem of these operators is investigated. The rates of convergence of ...

Approximation by the Bernstein–Durrmeyer Operator on a Simplex

For the Jacobi-type Bernstein–Durrmeyer operator Mn,κ on the simplex T d of R , we proved that for f ∈ L(Wκ ;T ) with 1 <p <∞, K2,Φ ( f,n−1 ) κ,p ≤ c‖f −Mn,κf ‖κ,p ≤ c′K2,Φ ( f,n−1 ) κ,p + c′n−1‖f ‖κ,p, where Wκ denotes the usual Jacobi weight on T d , K2,Φ(f, t)κ,p and ‖ · ‖κ,p denote the second-order Ditzian–Totik K-functional and the L-norm with respect to the weight Wκ on T d , respectively...

q−BERNSTEIN-SCHURER-KANTOROVICH TYPE OPERATORS

The aim of this paper is to present a Stancu type Kantorovich modification of q−BernsteinSchurer operators introduced by Muraru [22] and modified by Ren and Zeng [29]. Here, we obtain a convergence theorem by using the well known Bohman-Korovkin criterion and find the estimate of the rate of convergence by means of modulus of continuity and Lipschitz function for these operators. Also, we estab...