The purpose of the present paper is to introduce a q-Durrmeyer variant of generalized-Bernstein operators proposed by Chen et al. (2017). The convergence rate of these operatorsis examined by means of the Lipschitz class and the Peetre’s K-functional. Also, we definethe bivariate case of these operators and study the degree of approximation with the aid of thepartial moduli of continuity and higher order modulus of continuity via Peetre’s K-functionalapproach. Finally, we introduce the GBS (Generalized Boolean Sum) of the considered operatorsand investigate the approximation of the B¨ogel continuous and B¨ogel differentiable functionswith the aid of the Lipschitz class and the mixed modulus of smoothness. Some numericalexamples with illustrative graphics have been added to validate the theoretical results and alsocompare the rate of convergence by using Matlab algorithms.
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