*Article* **Durrmeyer-Type Generalization of Parametric Bernstein Operators**

### **Arun Kajla 1, Mohammad Mursaleen 2,3,4,\* and Tuncer Acar 5**


Received: 13 June 2020; Accepted: 6 July 2020; Published: 8 July 2020

**Abstract:** In this paper, we present a Durrmeyer type generalization of parametric Bernstein operators. Firstly, we study the approximation behaviour of these operators including a local and global approximation results and the rate of approximation for the Lipschitz type space. The Voronovskaja type asymptotic formula and the rate of convergence of functions with derivatives of bounded variation are established. Finally, the theoretical results are demonstrated by using MAPLE software.

**Keywords:** Bernstein operators; rate of approximation; Voronovskaja type asymptotic formula
