**8. Conclusions**

We have introduced generalized Bernstein–Durrmeyer type operators depending on non-negative integers. We developed many approximation properties such as local and global approximation, the rate of approximation for the Lipschitz type space, Voronovskaja type asymptotic formula and the rate of convergence of functions with derivatives of bounded variation. The constructed operators have better flexibility and rate of convergence which are depending on the selection of the *ρ*1, *ρ*2 and *θ*. Graphical representations of our operators for different selections of *ρ*1, *ρ*2 and *θ* are also given.

**Author Contributions:** Project administration, M.M.; Writing—original draft, A.K.; Writing—review and editing, T.A. & M.M. The authors contributed equally and significantly in writing this paper. All authors have read and agreed to the published version of the manuscript.

**Funding:** The third author has been partially supported within TUBITAK (The Scientific and Technological Research Council of Turkey) 1002-Project 119F191.

**Conflicts of Interest:** The authors declare no conflict of interest.
