The main motivation of this paper is to provide a generalization of Bernstein‐Chlodowsky type operators which depend on function τ by means of two sequences of functions. The newly defined operators fix the test function set {1, τ, τ²}. Then we present the approximation properties of newly defined operators, such as weighted approximation, degree of approximation and Voronovskaya type theorems. Finally, we present a series of numerical examples demonstrating the effectiveness of this newly defined Bernstein‐Chlodowsky operators for computing function approximation.

中文翻译：

---

通过新构造的Bernstein-Chlodowsky算子来逼近函数：理论和应用

本文的主要动机是通过两个函数序列提供依赖于函数τ的Bernstein-Chlodowsky型算子的概括。新定义的操作符固定测试功能组{1，  τ，  τ ² }。然后，我们介绍新定义的算子的逼近性质，例如加权逼近，逼近度和Voronovskaya型定理。最后，我们提供了一系列数值示例，证明了这个新定义的Bernstein-Chlodowsky算子对于计算函数逼近的有效性。