基于Pochhammer k符号的Lupaş-Beta算子逼近性质  

Approximation Properties of Lupas-Beta Operators Based on Pochhammer k-Symbol

作　　者：程文韬 刘玉洁 杨瑞 华义平 CHENG Wentao;LIU Yujie;YANG Rui;HUA Yiping(School of Mathematics and Physics,Anqing Normal University,Anqing 246133,China;College of Big Date and Artificial Intelligence,Chizhou University,Chizhou 247000,China)

机构地区：[1]安庆师范大学数理学院,安徽安庆246133 [2]池州学院大数据与人工智能学院,安徽池州247000

出　　处：《安庆师范大学学报（自然科学版）》2024年第1期24-29,共6页Journal of Anqing Normal University(Natural Science Edition)

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：参数型基函数曲线曲面造型的应用与相应算子的结构性质和收敛性质被广泛关注。为此,本文首次利用Beta函数,构造了一种基于Pochhammer k符号的Lupas-Beta含幂参数型算子。同时,利用中心矩研究了该算子的Voronovskaya型渐进公式,根据Ditzian-Totik光滑模和Peetre’-K泛函讨论了其全局逼近,并借助函数的分解技巧和区间分割技术等研究了其关于导数为有界变差函数的点态估计。本研究将为该算子在曲线曲面造型中的应用提供关键的理论依据。The application of curve and surface modeling of parametric basis functions,and the structural properties and convergence properties of the corresponding operators have attracted extensive attention from scholars at home and abroad.Therefore,in this paper,a type of Lupas-Beta screen parameter operators based on Pochhammer k-symbol is constructed by using Beta function for the first time.The Voronovskaya type asymptotic formula of the operators is studied using center moment,the global approximation of the operators is discussed according to Ditzian-Totik moduli of smoothness and Peetre’Kfunctional,the pointwise estimate of the operators in terms of derivatives being bounded variation functions is studied by combining it with decomposition technique of functions and interval division technique.The research in this paper will provide the key theoretical basis for the application of this operator in curve and surface modeling.

关 键 词：Lupas-Beta算子 Pochhammer k符号 全局逼近 有界变差函数 

分 类 号：O174.41[理学—数学]