The goal of this paper is to develop a framework that would allow one to solve the problems of optimal recovery of the monotone operators that act on a possibly most extensive class of monotone functions. The results of this work allow us to include the operators that act on the spaces of multi- and fuzzy- valued functions, as well as on the spaces of functions with values in partially ordered normed spaces. As an application of the obtained results, we solve the problem of optimal recovery of the solution for the Volterra and Fredholm integral equations for function with values in partially ordered L-spaces, given information about the values of the known function in a finite number of points.

本文的目的是开发一个框架，该框架将使人们能够解决作用于可能最广泛的单调函数类的单调算符的最佳恢复问题。这项工作的结果使我们可以包括对多值和模糊值函数的空间以及部分有序赋范空间中的值的函数空间起作用的算子。作为获得的结果的一种应用，我们给出了具有有限阶L空间中值的函数的Volterra和Fredholm积分方程的解的最优恢复问题，该函数具有部分有序L空间中的值。点。