$L^{p}([0, 1]), 1\le p \le +\infty$中次线性、单调和强平移算子的定量Korovkin定理
Quantitative Korovkin theorems for sublinear, monotone and strongly translatable operators in $L^{p}([0, 1]), 1\le p \le +\infty$
摘要：
通过将Berens和DeVore在1978年和Swetits和Wood在1983年的$L^{p}([0, 1]), 1\le p \le +\infty$中关于正算子和线性算子的经典定量逼近结果推广到次线性、单调和强平移算子的更一般情况，本文得到了Korovkin型定理中关于二阶和三阶光滑模的定量估计.具体的例子中的应用和一个开放的问题，提出了次线性，单调和强平移算子的插值理论。
英文摘要：
By extending the classical quantitative approximation results for positive and linear operators in $L^{p}([0, 1]), 1\le p \le +\infty$ of Berens and DeVore in 1978 and of Swetits and Wood in 1983 to the more general case of sublinear, monotone and strongly translatable operators, in this paper we obtain quantitative estimates in terms of the second order and third order moduli of smoothness, in Korovkin type theorems. Applications to concrete examples are included and an open question concerning interpolation theory for sublinear, monotone and strongly translatable operators is raised.
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