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Modified $$\alpha $$ α -Bernstein–Durrmeyer-Type Operators
Iranian Journal of Science and Technology, Transactions A: Science  (IF),  Pub Date : 2021-08-16, DOI: 10.1007/s40995-021-01197-y
Agrawal, P. N., Kajla, Arun, Singh, Sompal

In this paper, we construct a Durrmeyer variant of the modified \(\alpha \)-Bernstein-type operators introduced by Kajla and Acar (Ann Funct Anal 10(4):570–582, 2019), for \(\alpha \in [0,1]\). We investigate the degree of approximation via the approach of Peetre’s K-functional and the Lipschitz-type maximal function. The quantitative Voronovskaja- and Grüss Voronovskaja-type theorems are discussed. Further, we determine the rate of convergence by the above operators for the functions with derivatives of bounded variation.