Modified Bernstein–Durrmeyer Type Operators

We constructed a summation–integral type operator based on the latest research in linear positive operators area. establish some approximation properties for this new operator. highlight qualitative part of presented operator; we studied uniform convergence, Voronovskaja-type theorem, and Grüss–Voronovskaja result. Our subsequent study focuses direct theorem using Ditzian–Totik modulus smoothness order functions belonging to Lipschitz-type space. For complete image quantitative estimations, included convergence rate differential functions, whose derivatives were bounded variations. In last section article, present two graphs illustrating convergence.