基于Riemann-Liouville分数阶积分Bernstein-Kantorovich算子的逼近性质  

Approximation Properties of Bernstein-Kantorovich Operators Based on Riemann-Liouville Fractional Integration

作　　者：汪洋 程文韬 刘玉洁 刘磊 WANG Yang;CHENG Wentao;LIU Yujie;LIU Lei(School of Mathematics and Physitcs,Anqing Normal University,246133,Anqing,Anhui,China)

机构地区：[1]安庆师范大学数理学院,安徽安庆246133

出　　处：《淮北师范大学学报（自然科学版）》2024年第1期27-32,共6页Journal of Huaibei Normal University：Natural Sciences

基　　金：国家自然科学基金项目(11626031);安徽省自然科学基金项目(1908085QA29);安徽省高校自然科学研究重点项目(KJ2021A0648,KJ2019A0572)。

摘　　要：文章构造一种基于Riemann-Liouville分数阶积分的Bernstein-Kantorovich算子。利用一阶、二阶光滑模、Peetre’-K泛函和Lipschitz型极大函数等工具研究该算子的近似性质。然后利用一阶、二阶和四阶中心矩对该算子建立Vorononskaja型渐进公式。该算子的构建使得在曲线曲面造型方面对于给定的函数将会有更小的近似误差。A Bernstein-Kantorovich operator based on the Riemann-Liouville fractional integral is construct-ed.The approximate properties of the operator are investigated using the tools including first and second or-der smooth modulus of smoothness,Peetre’-K functional and Lipschitz type maximal function.Then the Vo-rononskaja type asymptotic formula is established by using the first,second and fourth order central moments for the operator.The construction of the operator causes a smaller approximation error for a given function in curve and surface modeling.

关 键 词：BERNSTEIN-KANTOROVICH算子 Riemann-Liouville分数阶积分 Peetre’-K泛函 Vorononskaja定理 

分 类 号：O174.41[理学—数学]