In the present manuscript, we consider ?-Bernstein-Durrmeyer operators involving a strictly positive continuous function. Firstly, prove Voronovskaja type, quantitative type and Gr?ss-Voronovskaja asymptotic formula, rate of convergence by means modulus continuity for functions in Lipschitz space. Finally, show that numerical examples which describe validity theoretical example effectiveness de...

In the present paper, we introduce the Durrmeyer variant of Baskakov-Bezier operators Bn,α(f, x), which is the modified form of Baskakov-Beta operators. Here we obtain an estimate on the rate of convergence of Bn,α(f, x) for functions of bounded variation in terms of Chanturiya’s modulus of variation. In the end we also propose an open problem for the readers.

Deo [5] introduced n-th Durrmeyer operators defined for functions integrable in some interval I. There are gaps and mistakes in some of his lemmas and theorems. Further, in his paper [4] he did not give results on simultaneous approximation as the title reveals. The purpose of this paper is to correct those mistakes. AMS subject classifications: 41A25, 41A30

A new class of differential operators on the simplex is introduced, which define weighted Sobolev norms andwhose eigenfunctions are orthogonal polynomialswith respect to Jacobiweights. These operators appear naturally in the study of quasi-interpolants which are intermediate between Bernstein– Durrmeyer operators and orthogonal projections on polynomial subspaces. The quasi-interpolants satisfy...

In this paper, we construct a form of linear positive operators with Brenke type polynomials as a generalization of Szasz-Durrmeyer operators. We obtain convergence properties of our operators with the help of the universal Korovkin-type property and calculate the order of approximation by using classical modulus of continuity. Explicit examples of our operators involving some orthonogal and d-...

In [10], for continuous functions f from the domain of certain discrete operators Ln the inequalities are proved concerning the modulus of continuity of Lnf . Here we present analogues of the results obtained for the Durrmeyer-type modification ̃ Ln of Ln. Moreover, we give the estimates of the rate of convergence of ̃ Lnf in Hölder-type norms