左拟中插式Gamma算子在Orlicz空间中的逼近性质

摘要: 为了得到更快的逼近速度，人们开始研究算子的拟中插式的逼近性质.在Orlicz空间中讨论左拟中插式Gamma算子的逼近性质，利用了Ditzian-Totik模与K-泛函的等价性、Hölder不等式、Cauchy-Schwarz不等式和Laguerre多项式等等工具得到了逼近的正、逆和等价定理，推广了左拟中插式Gamma算子在L_p空间中的逼近结果，改进了Gamma算子在Orlicz空间的逼近性质.
- 左拟中插式Gamma算子 /
- K-泛函 /
- 连续模 /
- 等价定理
Abstract: In order to reach better approximation degree, people start to study the quasiinterpolants of operators. In this paper, approximation properties of left quasi-interpolants Gamma operators are discussed by the tools of Ditizan-Totik modulus, K-functional, Hölder's inequality, Cauchy-Schwarz's inequality and Laguerre polynomials and so on. Then we obtain the direct, inverse and equivalence theorems which generalize the results of left quasi-interpolants Gamma operators in L_p space and improve the approximation properties of Gamma operators in Orlicz spaces.
- left quasi-interpolants Gamma operator /
- K-functional /
- modulus of smoothness /
- equivalence theorem

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参考文献(16)

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