一般Gamma型算子在Orlicz空间内的逼近  

Approximation of General Gamma Type Operators in Orlicz Spaces

作　　者：刘倩 吴嘎日迪[1,2] LIU Qian;WU Garidi(College of Mathematics Science,Inner Mongolia Normal University,Hohhot 010022,China;Inner Mongolia Center for Applied Mathematics,Hohhot 010022,China)

机构地区：[1]内蒙古师范大学数学科学学院,内蒙古呼和浩特010022 [2]内蒙古自治区应用数学中心,内蒙古呼和浩特010022

出　　处：《内蒙古师范大学学报（自然科学汉文版）》2023年第6期601-605,共5页Journal of Inner Mongolia Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11761055);内蒙古师范大学基本科研业务费专项资金资助项目(2023JBZD007)。

摘　　要：讨论一般Gamma型算子在Orlicz空间内的逼近问题,由于Orlicz空间比连续函数空间和Lp空间“大”,范数结构也比Lp空间复杂,所以在Orlicz空间内研究Gamma算子的逼近问题具有一定的拓展性。借助Cauchy⁃Schwarz不等式、Jensen不等式、光滑模和N函数的凸性等,证明一般Gamma型算子在Orlicz空间内的有界性,给出该算子在Orlicz空间内的逼近正定理。The approximation problems of general Gamma type operators in the Orlicz space is discussed.Since the Orlicz space is"larger"than the space of continuous function and Lp space,and its norm structure is much more complex than the Lp space,it is definitely of expansiveness to study the approximation problem of the Gamma operator in the Orlicz space.By using the Cauchy⁃Schwarz inequality,the Jensen inequality,the modulus of smoothness,convexity of the N function and other tools,the boundedness of general gamma⁃type operators in Orlicz spaces is proved,and then the approximation theorem of general Gamma⁃type operators in Orlicz spaces is given.

关 键 词：Gamma型算子 光滑模 K泛函 ORLICZ空间 

分 类 号：O174.41[理学—数学]