保持函数$e^{-\mu x}\left(\mu >0\right)$的Baskakov型算子的逼近性质

Approximation Properties of Baskakov Type Operators Preserving Function $e^{-\mu x}\left(\mu >0\right)$

摘要: 本文利用复合的思想，构造了保持函数$e^{-\mu x}\left(\mu >0\right)$ 的Baskakov型算子，给出了该类含参算子基函数图像，同时研究了该类算子的保单调性、保凸性、保星形性以及保半可加性。最后，选取适当的函数，利用数学软件绘制出该类算子的逼近效果图像，并给出逼近的均方根误差。

Abstract: In this paper, using the idea of combination, Baskakov operators maintaining the function $e^{-\mu x}\left(\mu >0\right)$ are constructed. The graphics of their basis functions are given. At the same time, the shape preserving properties of these operators are obtained in terms of monotonicity, convexity, starshapeness and semi-additivity. Finally, choosing the approximation function, the approximation effect image of these kind of operators are drawn by software, and the root mean square error of approximation is obtained.