Approximation of some classes of set-valued periodic functions by generalized trigonometric polynomials

TL;DR

This paper extends classical approximation results for periodic functions to set-valued functions, providing new bounds for best, linear, and one-sided approximations using generalized trigonometric polynomials.

Contribution

It generalizes existing approximation theories from scalar to set-valued periodic functions using convolution representations.

Findings

New bounds for approximation errors of set-valued functions

Extension of classical approximation results to set-valued functions

Generalized trigonometric polynomials effectively approximate set-valued functions

Abstract

Generalizations of some known results on the best, best linear and best one-sided approxima- tions by trigonometric polynomials of the classes of 2\pi - periodic functions presented in the form of convolutions to the case of set-valued functions are obtained