论文标题
Korneichuk-Stechkin引理，Ostrowski和Landau不平等，以及$ L $空间有价值功能的最佳恢复问题
Korneichuk-Stechkin Lemma, Ostrowski and Landau inequalities, and optimal recovery problems for $L$-space Valued Functions
论文作者
论文摘要
我们证明了korneichuk-stechkin引理的类似物，用于$ l $ - 空间的函数。作为应用程序，我们在$ l $ -space值的函数的类别上获得了敏锐的Ostrowski类型不等式，并解决了身份和共恢复运算符的最佳恢复问题以及整体恢复的问题。恢复是基于$ n $在某些时间间隔内的函数的平均值完成的。此外，在具有给定的Hukuhara类型衍生物的连续性模量的功能类别上，我们解决了该函数的最佳恢复和Hukuhara型衍生物的问题。恢复是基于该功能的$ n $值完成的。我们还获得了一些尖锐的Landau类型的不平等现象，并解决了由有限操作员近似无界操作员近似的Stechkin问题的类似物，以及在一类元素上，无限型操作员最佳恢复的问题，已知错误。考虑$ l $ - 空间有价值功能为多种和模糊值函数类别以及具有BANACH空间中值的函数类别（特别是随机过程，尤其是其他类别的功能）提供了一种统一的方法来解决上述极端问题的解决方案。
We prove an analogue of the Korneichuk--Stechkin lemma for functions with values in $L$-spaces. As applications, we obtain sharp Ostrowski type inequalities and solve problems of optimal recovery of identity and convexifying operators, as well as the problem of integral recovery, on the classes of $L$-space valued functions with given majorant of modulus of continuity. The recovery is done based on $n$ mean values of the functions over some intervals. Moreover, on the classes of functions with given majorant of modulus of continuity of their Hukuhara type derivative, we solve the problem of optimal recovery of the function and the Hukuhara type derivative. The recovery is done based on $n$ values of the function. We also obtain some sharp Landau type inequalities and solve an analogue of the Stechkin problem about approximation of unbounded operators by bounded ones and the problem of optimal recovery of an unbounded operator on a class of elements, known with error. Consideration of $L$-space valued functions gives a unified approach to solution of the mentioned above extremal problems for the classes of multi- and fuzzy-valued functions as well as for the classes of functions with values in Banach spaces, in particular random processes, and many other classes of functions.
