一类推广的Kantorovic型算子对不连续函数的逼近

Approximation of Discontinuous Functions by A Kind of Generalized Kantorovic Operators

通过研究一类推广的Kantorovic型算子Pn*(f,x)对不连续函数的逼近,得到了有界Lebeague可积函数的第一类间断点在区间[0,1]上收敛的充分条件,并给出了有界变差函数收敛度的估计式.

In this paper, the problems of convergence and approximation degree by a kind of generalized Kantorovic operators Pn^＊（f,x） are studied. A sufficient condition for convergence in interval [0,1] of the first discontinuous point about a bounded integrable Lebeague function is obtained, and an estimation of convergence index about a bounded variation function is founded.