修正的Picard算子在Orlicz空间中的指数加权逼近  

Exponential Weighted Approximation of Modified Picard Operators in Orlicz Spaces

作　　者：姜胜楠 吴嘎日迪[1,2] JIANG Shengnan;WU Garidi(College of Mathematics Science,Inner Mongolia Normal University,Hohhot 010022,China;Center of Applied Mathematicse,Inner Mongolia Autonomous Region,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：《应用数学》2023年第3期631-639,共9页Mathematica Applicata

基　　金：国家自然科学基金资助项目(11761055);内蒙古师范大学硕士研究生科研创新基金资助项目(CXJJS21121)。

摘　　要：本文研究修正的Picard算子在Orlicz空间内指数加权逼近的收敛性和逼近性质.通过建立Orlicz空间内指数加权逼近的相关引理,利用H?lder不等式,Korovkin定理,凸函数的Jensen不等式,Minkowski不等式及相关分析技巧得出该算子在Orlicz空间中指数加权逼近的正定理及相关性质.In this paper,we study the convergence and approximation properties of the modified Picard operator in the Orlicz spaces with respect to the exponential weight.We obtain the positive theorem of exponential weighted approximation of the modified Picard operator in Orlicz spaces and the related properties by the properties of the established Orlicz exponential weighted spaces and related lemmas,the H?lder inequality,the Korovkin theorem,the Jensen inequality of convex functions,the Minkowski inequality and some related analysis skills.

关 键 词：Picard算子 指数加权逼近 ORLICZ空间 

分 类 号：O174.41[理学—数学]