Durrmeyer-type generalization of $\mu$-Bernstein operators

Arun Kajla, S. M. Mohiuddine, Abdullah Alotaibi


In the present manuscript, we consider $\mu$-Bernstein-Durrmeyer operators involving a strictly positive continuous function. Firstly,  we prove a Voronovskaja type, quantitative Voronovskaja type and Gr\"uss-Voronovskaja type asymptotic formula, the rate of convergence by means of the modulus of continuity and for functions in a Lipschitz type space.  Finally, we show that the numerical examples which describe the validity of the theoretical example and the effectiveness of the defined operators.


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