# Bounds on strong unicity for Chebyshev approximation with bounded coefficients

## TL;DR

This paper derives new effective bounds on the uniqueness and stability of Chebyshev approximation with bounded coefficients using proof mining techniques and Lagrangian interpolation, extending previous results.

## Contribution

It introduces novel bounds on strong unicity constants for Chebyshev approximation with bounded coefficients, employing proof mining and Schur polynomial methods.

## Key findings

- New bounds on moduli of uniqueness
- Effective constants for strong unicity
- Extension to zero-restricted coefficients

## Abstract

We obtain new effective results in best approximation theory, specifically moduli of uniqueness and constants of strong unicity, for the problem of best uniform approximation with bounded coefficients, as first considered by Roulier and Taylor. We make use of techniques from the field of proof mining, as introduced by Kohlenbach in the 1990s. In addition, some bounds are obtained via the Lagrangian interpolation formula as extended through the use of Schur polynomials to cover the case when certain coefficients are restricted to be zero.