二元(p, q)-Bernstein算子的逼近性质
Approximation Properties of Bivariate (p, q)-Bernstein Operators
DOI: 10.12677/AAM.2020.92028, PDF,    科研立项经费支持
作者: 高 盼, 刘辉辉, 冷献祥：巢湖学院数学与统计学院，安徽 合肥
关键词: 二元(p； q)-Bernstein算子；收敛速度；Lipschitz函数；Bivariate (p； q)-Bernstein Operators； Rate of Convergence； Lipschitz Function
摘要: 本文在(p, q)-Bernstein算子的基础上构建二元(p, q)-Bernstein算子，证明该算子的逼近定理；应用Volkov定理验证了该算子的一致收敛性，并估计其收敛速度，此结论推广了一元(p, q)-Bernstein算子的逼近结果。
Abstract: In this paper, we introduce the bivariate (p, q)-Bernstein operator on the basis of (p, q)-Bernstein operator, and obtain the approximation theorem of the operator. The uniform convergence of the operator is verified by applying Volkov theorem, and its convergence rate is estimated. Those re-sults further promote some of the conclusions of (p, q)-Bernstein operator.
文章引用：高盼, 刘辉辉, 冷献祥. 二元(p, q)-Bernstein算子的逼近性质[J]. 应用数学进展, 2020, 9(2): 244-250. https://doi.org/10.12677/AAM.2020.92028

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