On Approximation Properties of Generalized Durrmeyer Operators

The concern of this paper is to introduce new generalized Durrmeyer-type operators from which classical operators can be obtained as a particular case, inspiring from the Ibragimov–Gadjiev operators (Gadjiev and Ibragimov, Soviet Math. Dokl. 11, 1092–1095, (1970) [8]).After the construction of newDurrmeyer operators is given, we obtain some pointwise convergence theorems and Voronovskaya-type asymptotic formula for new Durrmeyer-type operators. We establish a quantitative version of the Voronovskaya-type formula with the aid of the weighted modulus of continuity. Some special cases of new operators are presented as examples.