Abstract Approximation using linear positive operators is a well-studied research area. Many operators and their generalizations are investigated for their better approximation properties. In the present paper, we construct and investigate a variant of modified (p,q)(p,q)-Baskakov operators, which reproduce the test function x2x^{2}. We have determined the order of approximation of the operators via K-functional and second order, the usual modulus of continuity, weighted and statistical approximation properties. In the end, some graphical results which depict the comparison with (p,q)(p,q)-Baskakov operators are explained and a Voronovskaja type result is obtained.

中文翻译：

---

基于(𝑝, 𝑞) 演算的 Baskakov 算子的 King 型泛化具有更好的逼近性质

摘要 使用线性正算子的逼近是一个经过充分研究的研究领域。研究了许多算子及其泛化，以获得更好的近似特性。在本论文中，我们构建并研究了修改后的 (p,q)(p,q)-Baskakov 算子的变体，它再现了测试函数 x2x^{2}。我们已经通过 K 泛函和二阶、通常的连续性模数、加权和统计逼近属性来确定算子的逼近阶数。最后，解释了一些描述与 (p,q)(p,q)-Baskakov 算子比较的图形结果，并获得了 Voronovskaja 类型的结果。