A SIMPLE PROOF OF ITERATED LIMIT FOR VARIATION DIMINISHING OPERATOR OF SPLINE FUNCTIONS
样条变差缩减算子迭代极限的一个简单证明

The iterated limit for the variation diminishing operator of spline functions was de-termined by Hu and Xu by using the related results of Markov chain.In this paper,bythe method used in3],not only the proofs in1]and2]are considerably simplified,but also the convergence rate of the iterated limit is given.Furthermore,the error esti-mate given here for the cubic spline on a uniform partition in a certain sense is the best.