一类新线性正算子的Steckin-Marchaud型不等式

Steckin-Marchaud type inequalities for a new linear positive operator

在Lp[0，∞）（1≤P≤∞）空间中讨论Agrawal和Thamer所定义的一类线性正算子，借助Ditzian-Totik光滑模ωφ^2（f，t）p，利用Wickeren的思想得到了该算子逼近的弱型逆向不等式，即Steckin—Marchaud型不等式，从而给出了算子逼近的等价定理．

The approximation by a new linear positive operator, which was defined by Agrawal and Thamer, was discussed in Lp[0, ∞）（1 ≤ p ≤ ∞） spaces. With the ideas of Wickeren, the converse inequalities of the weak-type （Steckin-Marchaud type inequalities） were obtained by using of the modulus of smoothness ωφ^2（f, t）p. Finally, the equivalent theorems for approximation were given .