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

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.

Some approximation properties by a class of bivariate operators

“…Let . The GBS operator associated to a linear operator is defined as During time some researchers constructed and studied different type of GBS operators as we can see for example papers in Bărbosu et al, Kajla and Miclăuş, and Ruchi et al…”

“…exists and is finite. During time some researchers constructed and studied different type of GBS operators as we can see for example papers in Bȃrbosu et al, 18 Kajla and Miclȃuş, 19 and Ruchi et al 20 Let f ∈ C b (I 2 ). The GBS operator G M n,m associated to B M n,m can be introduced as follows…”

On Stancu type generalization of (p,q)-Gamma operators

“…In [18], Cheng, Zhang and Cai introduced (p, q)-analogue of Gamma operators preserving x 2 . Then, Stancu generalization of q-analogue operators or (p, q)-analogue operators have widely been discussed and investigated; see, e.g., [19,20,21,22]. All results motivate us to construct the stancu type generalization of (p, q)-Gamma operators (1.1).…”

Theq-Chlodowsky andq-Szasz-Durrmeyer Hybrid Operators on Weighted Spaces

“…He obtained the rate of convergence on weighted spaces and a Voronovskaya-type theorem for these operators. Some other studies based on classical q− theory are [17][18][19][20][21][22][23][24].…”