SOME RESULTS ON MULTIVARIATE POLYNOMIAL APPROXIMATIONS
关于多元多项式逼近的一些结果

This paper realizes first the multivariate algebraic and triangular polynomial approximations on $C(-\pi,\pi]^m\times -a,a]^k)$ with some general integral-type positive linearoperator. Then constructing certain specific product kernels, we have obtained the Rogosinski-type theorem of $m$dimensional triangular approximation on $C(-\pi,\pi]^m)$, and the Timan-type theorem of $k$-dimensional algebraic polynomial approximation on $C^r(-1,1]^k)$