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.
Positive linear operator, Durrmeyer-type operators, $GBS$ operator, $B$-continuous function, mixed modulus of continuity, $q$-integers
BARBOSU, DAN; ACU, ANA MARIA; and MURARU, CARMEN VIOLETA
"On certain GBS-Durrmeyer operators based on $q$-integers,"
Turkish Journal of Mathematics: Vol. 41:
2, Article 14.
Available at: https://journals.tubitak.gov.tr/math/vol41/iss2/14