K 阶 Sikkema-Kantorovi算子的 L_P 逼近

L_p—APPROXIMATION BY SIKKEMA—KANTOROVIC OPERATORS OF ORDER K

本文给出了 K 阶 Sikkema—Kantorovi(?)算子 LP 逼近的正反定理。文中用Ditzian—Totik 光滑模作为对函数光滑性的度量并利用了光滑模与 K—泛函的等价性。

In this paper,we proved direct and converse theorems for L_p—approxi-mation by so-called Sikkema—Kantorovic operators of order k which wasintroduced by Cao Jia Ding (曹家鼎) in [3].As an important tool for meas-uring the smootheness of a fanction we use the Ditzian-Totik modulus ofsmoothness and its equivalence to some approprate K—functionals.