Upper bounds of best one-sided approximations of the classes WrLΨ in the metric of L

Abstract

The lowest upper bound is obtained for best one-sided approximations of classes (r=1,2 ...) by trigonometric polynomials and splines of minimum deficiency with equidistant knots, in the metric of space L, where WrLΨ={f:f(x+2π)=f(x), f(r−1)(x) is absolutely continuous, ∥f(r)∥LΨ⩽1} and LΨ is an Orlicz space.