MULTI APPROXIMATION OF 3-MONOTONE BY CONVEX PIECEWISE POLYNOMIAL

Abstract

We take into consideration piecewise polynomials with defined knots for the 3-monotone multi approximation. The aim of this paper is to demonstrate that any piecewisepolynomial that is convex can be changed in a manner that makes it interpolate the functionat the knots, the resulting difference between the two multi approximation errors is a constantfactor that is dependent solely on the knots, in other words, we prove that every piecewiseconvex polynomial can be interpolatory while preserving its uniform multi approximationdegree.