加权的Szász-Kantorovich-Bézier算子在Orlicz空间中的逼近等价定理（英文）

Equivalent Theorems of Approximation by Weighted Szász-Kantorovich-Bézier Operators in Orlicz Spaces

本文介绍了由Young函数生成的Orlicz空间L_Φ~*[0,∞),然后建立了修正的加权K-泛函与加权光滑模的等价定理,并利用它得到了加Jacobi权的Szász-Kantorovich-Bézier算子在Orlicz空间中逼近的正、逆和等价定理.

In this paper, the Orlicz spaces LΦ＊[0, ∞） which correspond to the Young function Φ（x） are introduced. The equivalence theorem between the modified weighted K-functional and the weighted modulus of smoothness is established. Finally, the direct, inverse and equivalent theorems of Szasz-Kantorovich-Bezier operators, which have the Jacobi weight function are given by the equivalence theorem between the K-functional and modulus of smoothness in Orlicz spaces.