On the uniqueness of best approximation in Orlicz spaces

TL;DR

This paper investigates the conditions under which best approximation in Orlicz spaces is unique, focusing on various convex functions and finite-dimensional approximation classes including Tchebycheff spaces.

Contribution

It provides new insights into the uniqueness of best approximation in Orlicz spaces for different convex functions and approximation classes.

Findings

Uniqueness conditions depend on the convex function  and approximation class.

Results include cases involving Tchebycheff spaces.

The study extends understanding of approximation in Orlicz spaces.

Abstract

We study uniqueness of best approximation in Orlicz spaces L$\Phi$, for different types of convex functions $\Phi$ and for some finite dimensional approximation classes of functions, where Tchebycheff spaces, and more general approximation ones, are involved