修正的LupasBaskakov算子及导数的正逆定理

The Direct and Inverse Theorems of Modified LupasBaskakov Operators and the Derivatives

利用Ditzian Totik光滑模ω2φλ(f,t)(0 λ 1)和K 泛函K2φλ(f,t2)之间的等价关系,讨论修正的Lupas Baskakov算子逼近的正逆定理,得到了逼近的等价结果,统一了点态(λ=1)和整体(λ=0)逼近等价定理;此外,研究了该算子导数与所逼近函数光滑性之间的关系,得到了其特征刻画定理.

By using of the equivalent relation between the DitzianTotik modulus of smoothness ω2φλ(f,t)(0λ1) and the Kfunctional K2φλ(f,t2),both the direct and inverse approximation theorems of modified LupasBaskakov operators are discussed,and the equivalent results are obtained,which combine the pointwise(λ=1 )and global(λ=0 )approximation equivalent theorems.Furthermore,the relations between the derivatives of the LupasBaskakov operators and the smoothness of the approximated functions are studied, which characterize the theorems.