Best approximation of certain classes of smooth functions on the real axis by splines of a higher order (Q803843)

This paper presents the upper bounds for the error estimates for the best approximations of the functions from the class \(W^ n_ p(R)\) on the real line, \(1\leq p\leq \infty\), by splines \(S_ m\), T or of order \(m^ p\) determined on the mesh T. The authors prove that the obtained bounds are exact for the case of \(p=1,2\) and \(\infty\).