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

作　　者：周观珍[1] 

机构地区：[1]浙江工商大学数学系,杭州310018

出　　处：《应用数学学报》2007年第1期146-158,共13页Acta Mathematicae Applicatae Sinica

基　　金：浙江省教育厅项目(020030431)资助项目.

摘　　要：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.

关 键 词：SHEPARD算子 L^P空间 逼近阶 等价性定理 

分 类 号：O174.41[理学—数学]