Bivariate ?, q -Bernstein–Kantorovich Operators and GBS Operators of Bivariate ?, q -Bernstein–Kantorovich Type

Qing-Bo Cai, Wen-Tao Cheng and Bayram Çekim
Additional contact information
Qing-Bo Cai: School of Mathematics and Computer Science, Quanzhou Normal University, Quanzhou 362000, China
Wen-Tao Cheng: School of Mathematics and Computation Sciences, Anqing Normal University, Anhui 246133, China
Bayram Çekim: Department of Mathematics, Faculty of Science, Gazi University, Beşevler, Ankara 06500, Turkey

Mathematics, 2019, vol. 7, issue 12, 1-18

Abstract: In this paper, we introduce a family of bivariate α , q -Bernstein–Kantorovich operators and a family of G B S (Generalized Boolean Sum) operators of bivariate α , q -Bernstein–Kantorovich type. For the former, we obtain the estimate of moments and central moments, investigate the degree of approximation for these bivariate operators in terms of the partial moduli of continuity and Peetre’s K -functional. For the latter, we estimate the rate of convergence of these G B S operators for B -continuous and B -differentiable functions by using the mixed modulus of smoothness.

Keywords: ? , q -Bernstein–Kantorovich operators; GBS operators; B -continuous functions; moduli of continuity; B -differentiable functions; mixed modulus of smoothness; q -integers (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/7/12/1161/pdf (application/pdf)
https://www.mdpi.com/2227-7390/7/12/1161/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:7:y:2019:i:12:p:1161-:d:293114

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().