Bounds on strong unicity for Chebyshev approximation with bounded coefficients

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