We construct the Baskakov–Kantorovich operators based on shape parameter \(\alpha\) by linking with Stancu operators to approximate functions over unbounded intervals. We establish local approximation results with the help of suitable modulus of continuity, \({\mathcal {K}}\)-functional and Lipschitz-type space. Further, we obtain the weighted approximation properties and calculate the rate of convergence with a view of weighted modulus of continuity of our newly defined operators. Moreover, we present several numerical results for viewing the convergence and illustrate the error of approximation of aforesaid operators.

中文翻译：

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Baskakov–Kantorovich算子与Stancu算子链接的参数化逼近

我们通过与Stancu运算符链接以在无穷区间近似函数来基于形状参数\（\ alpha \）构造Baskakov–Kantorovich运算符。我们借助合适的连续模数，\（{\ mathcal {K}} \） -函数和Lipschitz型空间来建立局部逼近结果。此外，我们获得加权逼近性质，并根据新定义算子的加权连续模量来计算收敛速度。此外，我们提出了一些数值结果以观察收敛性，并说明了上述算子的近似误差。