Best Approximation by the Inverse of a Monotone Polynomial and the Location Problem Original Research Article

Let L={f∈C[0, 1]: f is non-decreasing, f(0)=0 and f(1)=1}. Let M be a class of monotone polynomials of degree n or less. Then each f∈L has a unique best uniform (or L1) approximation from {p−1: p∈M∩L}. The special case for M=Pn shows that the single-data-point location problem for a one-dimensional domain has a unique solution (uniform or L1-norm).