The present paper deals with modifications of Bernstein, Kantorovich, Durrmeyer and genuine Bernstein–Durrmeyer operators. Some previous results are improved in this study. Direct estimates for these operators by means of the first and second modulus of continuity are given. Also the asymptotic formulas for the new operators are proved.

中文翻译：

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扰动的伯恩斯坦型算子

本文讨论了Bernstein，Kantorovich，Durrmeyer和真正的Bernstein-Durrmeyer算子的修改。这项研究改进了以前的一些结果。通过第一和第二连续模量给出了对这些算子的直接估计。还证明了新算子的渐近公式。