一类和积分型混合算子在L^p空间的逼近性质

Approximation properties for certain mixed summation-integral type operators in the L^p spaces

研究了以Baskakov和Beta为基函数的一类和积分型混合算子,得到了在Lp(1≤p≤∞)空间逼近的正、逆定理以及等价定理.利用统一光滑模ωφ2λ(f,t)(0≤λ≤1),得到了点态逼近的等价定理.

The mixed summation-integral type operators having Baskakov and Beta basis functions are studied. The direct, converse and equivalence theorems in the Lp（1≤p≤∞） spaces are obtained. Using the unified smooth modulus ω^2λφ （f, t） （0 ≤λ≤ 1）, the pointwise approximation equivalence theorems are also gotten.