summary:We introduce and study a one-parameter class of positive linear operators constituting a link between the well-known operators of S. N. Bernstein and their genuine Bernstein-Durrmeyer variants. Several limiting cases are considered including one relating our operators to mappings investigated earlier by Mache and Zhou. A recursion formula for the moments is proved and estimates for simultaneous approximation of derivatives are given.
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机译：摘要：我们引入并研究一类正线性算子，它构成S. N. Bernstein著名算子与其真正的Bernstein-Durrmeyer变体之间的链接。考虑了几种极限情况，其中一种情况使我们的运营商与Mache和Zhou先前研究的映射有关。证明了矩的递推公式，并给出了导数同时逼近的估计。
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