Best approximation by integer-valued functions Original Research Article

Given an integer function ff, the problem is to find its best uniform approximation from a set KK of integer-valued bounded functions. Under certain conditions on KK, the best extremal (maximal or minimal) approximation is identified. Furthermore, the operator mapping ff to its extremal best approximation is shown to be Lipschitzian with some constant CC or optimal Lipschitzian having the smallest CC among all such operators. The results are applied to approximation problems.