Szasz-Mirakjan-Durrmeyer算子基于形状参数$\lambda的逼近$

IF 0.7 Q2 MATHEMATICS
R. Aslan
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引用次数: 4

摘要

本文研究了形状参数λ∈[−1,1]λ∈[−1,1]的szasz - mirakjan - durrmeyer算子的几个近似性质。首先,我们得到了一些初步结果,如矩和中心矩。接下来,我们根据通常的连续模估计收敛阶,对于函数分别属于Lipschitz型类和Peetre的k泛函。同时,我们证明了加权空间上的一个Korovkin型逼近定理,并推导了这些算子的一个Voronovskaya型渐近定理。最后,用图形和近似表的误差比较了这些新定义算子对某些函数的收敛性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Approximation by Szasz-Mirakjan-Durrmeyer operators based on shape parameter $\lambda$
In this paper, we study several approximation properties of Szasz-Mirakjan-Durrmeyer operators with shape parameter λ∈[−1,1]λ∈[−1,1]. Firstly, we obtain some preliminaries results such as moments and central moments. Next, we estimate the order of convergence in terms of the usual modulus of continuity, for the functions belong to Lipschitz type class and Peetre's K-functional, respectively. Also, we prove a Korovkin type approximation theorem on weighted spaces and derive a Voronovskaya type asymptotic theorem for these operators. Finally, we give the comparison of the convergence of these newly defined operators to the certain functions with some graphics and error of approximation table.
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