ON K -MONOTONE APPROXIMATION IN LP

Abstract

In 1995 Kopotun [4], introduced a paper on k -monotone polynomial and spline approximation in P L , 0 < p < ¥ quasi norm . In this paper, we discuss the errors of approximation of k -monotone function by k - monotone interpolation . It turns out that any two k -monotone functions f and g , whose graphs intersect each other at certain ( sufficiently many ) points in [a,b], have to be "close" to each other in the sense that P f - g , has to be small .

Keywords

• k -monotone polynomial
• interpolation