Theoretical analysis demonstrates direct approximation and Voronovskaya theorems for alpha-Szasz-Durrmeyer operators, highlighting uniform convergence behavior in weighted function spaces.
We propose a Durrmeyer-type extension of the α-Szász-Mirakyan operators. By employing a unified approach based on the Lipschitz kind maximal function, weighted function spaces, and the Ditzian–Totik modulus of smoothness, we obtain several direct approximation results. Moreover, quantitative forms of Voronovskaya-type as well as Grüss–Voronovskaya-type theorems are obtained. The convergence properties of the introduced operators are also visualized and compared for certain functions with the aid of Maple software.
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Sehrawat et al. (2026) studied this question.
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