L^p空间Shepard算子逼近的正逆定理

Direct and Converse Approximation Theorems for the Shepard Operators in L^p Spaces

本文引入了一种修正的积分型Shepard算子,建立了相应的Jackson型定理,并通过建立Bernstein型不等式,给出了算子在L[0,1]p空间中一种新的逼近阶刻画的等价形式,得到了逼近的逆定理．

A kind of new equivalent theorem for the approximation by a kind of modified Kantorovich- Shepard operators in L[0,1]^p is established with the help of K-functional. Its direct and converse approximation theorems are obtained by establshing Bernstein type inequalities.