Local and global Lipschitz constants

AbstractLet X be a closed subset of I = [−1, 1], and let Bn(f) be the best uniform approximation to fϵ C[X] from the set of polynomials of degree at most n. An extended global Lipschitz constant is defined for f, and it is shown that this constant is asymptotically equivalent to the strong unicity constant. Estimates of the size of the local Lipschitz constant for f are given when the cardinality of the set of extremal points of f − Bn(f)is n + 2. Examples which illustrate that the local and extended global Lipschitz constants may have very different asymptotic behavior are constructed