Uniqueness of best Chebyshev approximations in spline subspaces (Q1070147)

This paper deals with the problem of uniqueness of best Chebyshev approximations by subspaces of spline functions on compact subsets T of \({\mathbb{R}}\). Necessary and sufficient conditions ensuring uniqueness of best approximations are given and a characterization of strongly unique best approximations using best approximations on finite subsets of T is established. Moreover, problems where a best approximation is unique on an interval I but is not a unique best approximation on any finite subset are considered.