Binomial operators are the most important extension to Bernstein operators, defined by $$ \bigl(L^{Q}_{n} f\bigr) (x)=\frac{1}{b_{n}(1)} \sum ^{n}_{k=0}\binom { n}{k } b_{k}(x)b_{n-k}(1-x)f\biggl( \frac{k}{n}\biggr),\quad f\in C[0, 1], $$ where $\{b_{n}\}$ is a sequence of binomial polynomials associated to a delta operator Q. In this paper, we discuss the binomial operators $\{L^{Q}_{n} f\}$ preservation such as smoothness and semi-additivity by the aid of binary representation of the operators, and present several illustrative examples. The results obtained in this paper generalize what are known as the corresponding Bernstein operators.

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关于二项式运算符的保留

二项式运算符是对Bernstein运算符的最重要扩展，定义为$$ \ bigl（L ^ {Q} _ {n} f \ bigr）（x）= \ frac {1} {b_ {n}（1）} \ sum ^ {n} _ {k = 0} \ binom {n} {k} b_ {k}（x）b_ {nk}（1-x）f \ biggl（\ frac {k} {n} \ biggr） ，\ quad f \ in C [0，1]，$$，其中$ \ {b_ {n} \} $是与增量算子Q相关的二项式多项式序列。在本文中，我们讨论二项式算子$ \借助于算子的二进制表示，保持{L ^ {Q} _ {n} f \} $，例如平滑度和半可加性，并给出几个说明性示例。本文获得的结果概括了所谓的相应伯恩斯坦算子。