Simultaneous approximation with generalized Durrmeyer operators

The aim of this paper is to obtain some convergence properties of generalized sequences of Ibragimov–Gadjiev–Durrmeyer operators which are a wide class of linear positive operators including many well known linear positive operators. Firstly, the Voronovskaya type theorem in simultaneous approximation is given. Then we present an upper estimate of norm convergence of the derivatives of the operators in quantitative mean in terms of the modulus of continuity. We show several of sequences that can be derived from them by means of a suitable transformation. Some special cases of new operators are presented as examples.