# A note on the best approximation in spaces of affine functions

## TL;DR

This paper investigates the proximinality of subspaces within spaces of bounded affine functions, providing linear analogs of Mazur's classical result using Fenchel's duality theory.

## Contribution

It introduces linear versions of an established approximation result for affine functions, employing Fenchel's duality for proofs.

## Key findings

- Proves proximinality of certain subspaces of bounded affine functions.
- Establishes linear analogs of Mazur's classical approximation result.
- Utilizes sandwich theorems from Fenchel's duality theory in proofs.

## Abstract

The proximinality of certain subspaces of spaces of bounded affine functions is proved. The results presented here are some linear versions of an old result due to Mazur. For the proofs we use some sandwich theorems of Fenchel's duality theory.