加权的Szász-Kantorovich-Bézier算子在Orlicz空间中的逼近等价定理（英文）  

Equivalent Theorems of Approximation by Weighted Szász-Kantorovich-Bézier Operators in Orlicz Spaces

作　　者：韩领兄[1] 吴嘎日迪[2] HAN Lingxiong;WU Garidi(Mathematics College,Inner Mongolia University for Nationalities,Tongliao,Inner Mongolia,028043,P.R.China;School of Mathematical Sciences,Inner Mongolia Normal University,Hohhot,Inner Mongolia,010021,P.R.China)

机构地区：[1]内蒙古民族大学数学学院,通辽内蒙古028043 [2]内蒙古师范大学数学科学学院,呼和浩特内蒙古010021

出　　处：《数学进展》2018年第5期719-734,共16页Advances in Mathematics（China）

基　　金：partially supported by NSFC(No.11461052)

摘　　要：本文介绍了由Young函数生成的Orlicz空间L_Φ~*[0,∞),然后建立了修正的加权K-泛函与加权光滑模的等价定理,并利用它得到了加Jacobi权的Szász-Kantorovich-Bézier算子在Orlicz空间中逼近的正、逆和等价定理.In this paper, the Orlicz spaces LΦ＊[0, ∞） which correspond to the Young function Φ（x） are introduced. The equivalence theorem between the modified weighted K-functional and the weighted modulus of smoothness is established. Finally, the direct, inverse and equivalent theorems of Szasz-Kantorovich-Bezier operators, which have the Jacobi weight function are given by the equivalence theorem between the K-functional and modulus of smoothness in Orlicz spaces.

关 键 词：ORLICZ空间 Jacobi权函数 Szász-Kantorovich-Bézier算子 K-泛函 光滑模 

分 类 号：O174.41[理学—数学]