The Limit of Biased Varisolvent Chebyshev Approximation

Abstract

AbstractBest biased and one-sided Chebyshev approximation with respect to a varisolvent approximating function on an interval are considered. The uniform limit of best biased approximations is the (unique) best one-sided approximation if the best one-sided approximation is of maximum degree. Examples are given where the best one-sided approximation is not of maximum degree and failure of uniform convergence and of existence occurs.