On Monotone Spline Approximation

Abstract

Listen

Translate article

The present paper shows that one cannot expect the Jackson type estimates to hold for higher degree moduli of smoothness in monotone (or comonotone) spline approximation. This result gives a complete negative answer to a question raised by DeVore for $m \geq 2$ in monotone spline approximation. It also indicates that an equivalence between monotone polynomial approximation and monotone spline approximation claimed by Wang is wrong in one direction. There are corresponding results in $L^p $ spaces.