二元(p, q)-Bernstein算子的逼近性质

Approximation Properties of Bivariate (p, q)-Bernstein Operators

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。

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.