Modified Bernstein–Durrmeyer Type Operators

Arun Kajla and Dan Miclǎuş
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Arun Kajla: Department of Mathematics, Central University of Haryana, Mahendragarh 123029, Haryana, India
Dan Miclǎuş: Department of Mathematics and Computer Science, Technical University of Cluj-Napoca, North University Center at Baia Mare, Victoriei 76, 430122 Baia Mare, Romania

Mathematics, 2022, vol. 10, issue 11, 1-13

Abstract: We constructed a summation–integral type operator based on the latest research in the linear positive operators area. We establish some approximation properties for this new operator. We highlight the qualitative part of the presented operator; we studied uniform convergence, a Voronovskaja-type theorem, and a Grüss–Voronovskaja type result. Our subsequent study focuses on a direct approximation theorem using the Ditzian–Totik modulus of smoothness and the order of approximation for functions belonging to the Lipschitz-type space. For a complete image on the quantitative estimations, we included the convergence rate for differential functions, whose derivatives were of bounded variations. In the last section of the article, we present two graphs illustrating the operator convergence.

Keywords: linear positive operators; uniform approximation; rate of convergence; modulus of continuity (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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