二元非乘积型Baskakov算子的某些逼近性质

Some Approximation Theorem of Two-Dimensional Baskakov Operators

该文利用多元分解技巧及一元的结果得出二元非乘积型算子 Vn的两个逼近性质定理 .对 f∈C0 ( T2 ) ,‖ Vn( f) - f‖≤cω2 ( f,1n) ;对 f∈ C2 ( T2 ) ,limn→∞n( Vn( f ) - f ) =x( 1 + x)2 f11+ y( 1 + y)2 f2 2 + xy2 f12 .

Making use of multivariate decompose skills and results of one dimensional Baskakov operators. It is abtained that \$f∈C\-0(T\+2),‖V\-n(f)-f‖≤cω\-2(f,1n);\$ and \$f∈C\+2(T\+2), lim n→∞n(V\-n(f)-f)=x(1+x)2f\-\{11\}+y(1+y)2f\-\{22\}+xy2f\-\{12\}.\$