Abstract
In the present paper, we introduce the Bezier-variant of Durrmeyer modification of the Bernstein operators based on a function \(\tau \), which is infinite times continuously differentiable and strictly increasing function on [0, 1] such that \(\tau (0)=0\) and \(\tau (1)=1\). We give the rate of approximation of these operators in terms of usual modulus of continuity and K-functional. Next, we establish the quantitative Voronovskaja type theorem. In the last section we obtain the rate of convergence for functions having derivative of bounded variation.
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Acar, T., Agrawal, P.N. & Neer, T. Bezier variant of the Bernstein–Durrmeyer type operators. Results Math 72, 1341–1358 (2017). https://doi.org/10.1007/s00025-016-0639-3
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DOI: https://doi.org/10.1007/s00025-016-0639-3