Some optimal recovery problems for operators on classes of $L$-space valued functions

TL;DR

This paper addresses optimal recovery problems for operators acting on classes of functions valued in $L$-spaces, which encompass multi-valued, fuzzy, and stochastic functions, providing a unified framework.

Contribution

It introduces solutions to three optimal recovery problems for operators on $L$-space valued functions, extending classical results to a broader class of functions.

Findings

Solved three optimal recovery problems for $L$-space valued functions

Unified treatment of multi-, fuzzy-valued functions and stochastic processes

Extended classical recovery results to semilinear metric spaces

Abstract

We solve three optimal recovery problems for operators on classes of $L$-space (which is a semilinear metric space with two additional axioms that connect the metric with the algebraic operations) valued functions that are defined by a majorant of their modulus of continuity. Consideration of $L$-spaces valued functions allows to treat multi- and fuzzy-valued functions, as well as random processes and other non-real valued functions in a unified manner.