Approximation of multivariate function by using new multivariate Bernstein α-polynomials

摘要

In this paper the approximation of multivariate function by using multivariate Bernstein α-polynomials is considered. The Bernstein α-polynomials are given and an identity is constructed. With these the well-known multivariate Bernstein approximation is expanded. The main result is for any continuous multivariate function f(x) there exist Bernstein α-polynomials {Bn(f,x,α)}n which converge to f(x) uniformly on a box set as n→∞.