Bivariate tensor product [Formula: see text]-analogue of Kantorovich-type Bernstein-Stancu-Schurer operators

Qing-Bo Cai; Xiao-Wei Xu; Guorong Zhou

doi:10.1186/s13660-017-1559-9

Bivariate tensor product [Formula: see text]-analogue of Kantorovich-type Bernstein-Stancu-Schurer operators

J Inequal Appl. 2017;2017(1):284. doi: 10.1186/s13660-017-1559-9. Epub 2017 Nov 14.

Authors

Qing-Bo Cai¹, Xiao-Wei Xu^{2

3}, Guorong Zhou⁴

Affiliations

¹ School of Mathematics and Computer Science, Quanzhou Normal University, Quanzhou, 362000 China.
² School of Mathematical Sciences, Xiamen University, Xiamen, 361005 China.
³ Computer Sciences, Rice University, Houston, USA.
⁴ School of Applied Mathematics, Xiamen University of Technology, Xiamen, 361024 China.

Abstract

In this paper, we construct a bivariate tensor product generalization of Kantorovich-type Bernstein-Stancu-Schurer operators based on the concept of [Formula: see text]-integers. We obtain moments and central moments of these operators, give the rate of convergence by using the complete modulus of continuity for the bivariate case and estimate a convergence theorem for the Lipschitz continuous functions. We also give some graphs and numerical examples to illustrate the convergence properties of these operators to certain functions.

Keywords: Bernstein-Stancu-Schurer operators; Lipschitz continuous functions; [Formula: see text]-integers; bivariate tensor product; modulus of continuity.