Nonexistence of best alternating approximations on subsets

Charles B. Dunham
1976 Proceedings of the American Mathematical Society  
The existence of best Chebyshev approximations by an alternating family on closed subsets of an interval is considered. In varisolvent approximation, existence on subsets of sufficiently low density is guaranteed if the best approximation on the interval is of maximum degree. The paper studies the case in which the best approximation is not of maximum degree and shows that in many common cases, no such guarantee is possible.
doi:10.1090/s0002-9939-1976-0417643-8 fatcat:dgutqekmpzcjjfdmduz75noaq4