Local Smoothness of Functions and Baskakov–Durrmeyer Operators Original Research Article

In this paper, we consider the local approximation by Baskakov–Durrmeyer operators. The continuous functions of local Lipschitz-α(0<α<1) on any subset of [0, ∞) are characterized by the local rate of convergence of Baskakov–Durrmeyer operators. The main difference between these operators and their classical and Kantorovich-variants respectively is that they have commutativity, which is crucial for our purpose.