Optimal Recovery of Monotone Operators in Partially Ordered L-Spaces
В. Ф. Бабенко, Vira Babenko, Oleg Kovalenko · Numerical Functional Analysis and Optimization · 2020
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.