B样条拟插值算子在Orlicz空间中的逼近  

Approximation of B-spline Quasi Interpolation Operators in Orlicz Spaces

作　　者：闫丽新 韩领兄[1] YAN Lixin;HAN Lingxiong(College of Mathematics Science,Inner Mongolia Minzu University,Tongliao 028043,China)

机构地区：[1]内蒙古民族大学数学科学学院,内蒙古通辽028043

出　　处：《内蒙古民族大学学报（自然科学版）》2024年第1期61-65,共5页Journal of Inner Mongolia Minzu University：Natural Sciences

基　　金：内蒙古自治区自然科学基金项目(2020LH01007)。

摘　　要：为了研究B样条拟插值算子在Orlicz空间的逼近性质,根据m阶B样条算子所构造出的B样条拟插值算子的定义,利用B样条算子的基本性质、Orliz空间的相关性质和光滑模、K泛函及其等价性质等工具,参照B样条拟插值算子在Lp空间逼近的研究方法对B样条拟插值算子进行了研究,得到B样条拟插值算子的有界性,最后得出B样条拟插值算子在Orlicz空间的逼近正定理。In order to study the approximation properties of the B-spline quasi-interpolation operator in the Orlicz space,according to the definition of the B-spline quasi-interpolation operator constructed by the m-order Bspline operator,the basic properties of the B-spline operator,the correlation properties of the Orliz space,the smooth modulus,the K-functional and its equivalence properties and other tools are used to study the B-spline qua⁃si-interpolation operator with reference to the research method of the B-spline quasi-interpolation operator in Lp space,the boundedness of the B-spline quasi-interpolation operator is obtained,and finally the approximation posi⁃tive theorem of the B-spline quasi-interpolation operator is obtained in Orlicz space.

关 键 词：B样条拟插值算子 ORLICZ空间 正定理 

分 类 号：O241.5[理学—计算数学]