Better approximation results by Bernstein–Kantorovich operators

被引：12

作者：

Dhamija M. ^{[1
]}

Deo N. ^{[1
]}

机构：

[1] Department of Applied Mathematics, Delhi Technological University (Formerly Delhi College of Engineering), Bawana Road, Delhi

来源：

Lobachevskii Journal of Mathematics | 2017年 / 38卷 / 1期

关键词：

Kantorovich; Rate of convergence; Voronovskaya;

D O I：

10.1134/S1995080217010085

中图分类号：

学科分类号：

摘要：

In this paper, we give a King-type modification of the Bernstein–Kantorovich operators and study the approximation properties of these operators. We prove that the error estimation of these operators is better than the classical Bernstein–Kantorovich operators. We also give some estimations for the rate of convergence of these operators by using the modulus of continuity. Furthermore, we obtain a Voronovskaya-type asymptotic formula for these operators. © 2017, Pleiades Publishing, Ltd.

引用

页码：94 / 100

页数：6

共 9 条

[1]

Butzer P.L., On two dimensional Bernstein polynomials, Canad. J. Math., 5, pp. 107-113, (1953)

[2]

de la Cal J., Carcamo J., Valle A.M., A best constant for bivariate Bernstein and Sz+asz-Mirakyan operators, J. Approx. Theory, 123, pp. 117-124, (2003)

[3]

Deo N., Bhardwaj N., Singh S.P., Simultaneous approximation on generalized Bernstein–Durrmeyer operators, Afrika Mat., 24, pp. 77-82, (2011)

[4]

Deo N., Noor M.A., Siddiqui M.A., On approximation by a class of new Bernstein type operators, Appl. Math. Comput., 201, pp. 604-612, (2008)

[5]

Derriennic M.M., Sur l’approximation de fonctions intégrables sur [0, 1] par des polynô mes de Bernstein modifies, J. Approx. Theory, 31, pp. 325-343, (1981)

[6]

Kantorovitch L.V., Sur certains développments suivant lés pô ynô mes déla forme S. Bernstein I, C. R. Acad. Sci. URSS, 20, pp. 563-568, (1930)

[7]

King J.P., Positive linear operators which preserve x <sup>2</sup> , Acta Math. Hungar., 99, pp. 203-208, (2003)

[8]

Stancu D.D., Approximation of functions by a new class of linear polynomial operators, Rev. Roum. Math. Pures Appl., 13, pp. 1173-1194, (1968)

[9]

Zhou D.X., Weighted approximation by multidimensional Bernstein operators, J. Approx. Theory, 76, pp. 403-422, (1994)

← 1 →