Abstract
The approximation properties of the Aldaz–Kounchev–Render (AKR) operators where investigated in several papers. We improve some existing quantitative results concerning these approximation properties. Moreover, we describe classes of functions for which these operators approximate better than the classical Bernstein operators and classes of functions for which Bernstein operators approximate better than AKR operators. The new results, in particular involving monotonic convergence and Voronovskaja type formulas, are then extended to the bivariate case on the square \([0,1]^2\) and compared with other existing results. Several numerical examples, illustrating the relevance and supporting the theoretical findings, are presented.
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Acknowledgements
This work has been accomplished within the Rete Italiana di Approssimazione and the UMI Group “Teoria dell’Approssimazione e Applicazioni”. The first author has been supported by the INdAM-GNCS Visiting Professors program 2021. The second author has been also partially supported by the Erasmus+ Programme for Teaching Staff Mobility between the Universities of Padova and Sibiu.
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Acu, AM., De Marchi, S. & Raşa, I. Aldaz–Kounchev–Render Operators and Their Approximation Properties. Results Math 78, 21 (2023). https://doi.org/10.1007/s00025-022-01793-3
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DOI: https://doi.org/10.1007/s00025-022-01793-3