Abstract
It is proved that an integrable functionf can be approximated by the Kantorovich type modification of the Szász—Mirakjan and Baskakov operators inL 1 metric in the optimal order {n −1} if and only ifϕ 2 f′ is of bounded variation where\(\varphi (x) = \sqrt x \) and\(\varphi (x) = \sqrt {x(1 + x)} \), respectively.
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Totik, V. Saturation of Kantorovich type operators. Period Math Hung 16, 115–126 (1985). https://doi.org/10.1007/BF01857591
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DOI: https://doi.org/10.1007/BF01857591