涉及Sheffer多项式的广义Szasz算子的逼近
Approximation by generalized Szasz operators involving Sheffer polynomials
摘要：
本文的目的是给出由Sheffer型多项式定义的Szasz算子的Chlodowsky型推广。利用Korovkin定理和二阶连续模及Peetre K-泛函，我们得到了算子的收敛性和收敛阶.此外，我们还研究了这类算子在正半轴上的加权函数空间中的收敛性，并利用Gadjiev和Aral在[12]中引入的一类新的加权连续模估计了其逼近.文中还给出了一个算法来绘制图形实例，并证明了这些算子对函数的收敛性，这些实例也可以作为新算子与前一算子的比较。最后给出了一些数值例子。
英文摘要：
The purpose of this article is to give a Chlodowsky type generalization of Szasz operators defined by means of the Sheffer type polynomials. We obtain convergence properties of our operators with the help of Korovkin's theorem and the order of convergence by using a classical approach, the second order modulus of continuity and Peetre's K-functional. Moreover, we study the convergence of these operators in a weighted space of functions on a positive semi-axis and estimate the approximation by using a new type of weighted modulus of continuity introduced by Gadjiev and Aral in [12]. An algorithm is also given to plot graphical examples, and we have shown the convergence of these operators towards the function and these examples can be take as a comparison between the new operators with the previous one too. Finally, some numerical examples are also given.
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