On certain GBS-Durrmeyer operators based on $q$-integers

Authors

DAN BARBOSU
ANA MARIA ACU
CARMEN VIOLETA MURARU

DOI

10.3906/mat-1601-34

Abstract

In the present paper we introduce the $GBS$ (Generalized Boolean Sum) operators of Durrmeyer type based on $q$-integers and the approximation of B-continuous functions using the above operators is studied. In addition, a uniform convergence theorem is established and the degree of approximation in terms of mixed modulus of continuity is evaluated. The study contains in the last section numerical considerations regarding the constructed operators based on MATLAB algorithms.

Keywords

Positive linear operator, Durrmeyer-type operators, $GBS$ operator, $B$-continuous function, mixed modulus of continuity, $q$-integers

First Page

368

Last Page

380

Recommended Citation

BARBOSU, DAN; ACU, ANA MARIA; and MURARU, CARMEN VIOLETA (2017) "On certain GBS-Durrmeyer operators based on $q$-integers," Turkish Journal of Mathematics: Vol. 41: No. 2, Article 14. https://doi.org/10.3906/mat-1601-34
Available at: https://journals.tubitak.gov.tr/math/vol41/iss2/14