λ-Kantorovich算子的逼近性质  

Approximation properties of λ-Kantorovich operators

作　　者：郭丹丹 齐秋兰[1,2] Guo Dandan;Qi Qiulan(School of Mathematical Sciences,Hebei Normal University,Shijiazhuang 050024,China;Hebei Key Laboratory of Computational Mathematics and Applications,Shijiazhuang 050024,China)

机构地区：[1]河北师范大学数学科学学院,河北石家庄050024 [2]河北省计算数学与应用重点实验室,河北石家庄050024

出　　处：《纯粹数学与应用数学》2020年第1期67-73,共7页Pure and Applied Mathematics

基　　金：国家自然科学基金(11571089,11871191);河北省教育厅资助项目(ZD2019053);河北师范大学研究生创新资助项目(CXZZSS2019059).

摘　　要：首先在无穷空间上构造了一类新的λ-Szász-Kantorovich算子,通过分析计算得到了该类算子矩的估计及Korovkin型逼近性质;其次,利用连续模和K-泛函的等价关系给出了收敛速度的刻画;最后,借助于Holder不等式建立了Lipschitz连续函数的收敛定理.Firstly,a new kind of λ-Szász-Kantorovich operator is constructed on infinite space,the moment estimation and Korovkin type approximation property of this kind of operator are obtained by analysis and calculation.Secondly,the convergence rate is obtained by using the equivalence relation between continuous module and K-functional.Finally,the convergence theorem of Lipschitz continuous function is established by using Holder inequality.

关 键 词：λ-Kantorovich算子 K-泛函 连续模 Lipschitz连续函数 

分 类 号：O175.41[理学—数学]