We investigate the weighted approximation of functions in \(L_p\)-norm by Kantorovich modifications of the classical Szász–Mirakjan operator, with weights of type \((1+x)^{\alpha }\), \(\alpha \in \mathbb {R}\). By defining an appropriate K-functional we prove direct inequality for them.

中文翻译：

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Szász-Mirakjan-Kantorovich 算子对函数的加权逼近

我们通过 Kantorovich 修改经典 Szász–Mirakjan 算子，研究\(L_p\) -norm中函数的加权逼近，权重类型为\((1+x)^{\alpha }\) , \(\alpha \在 \mathbb {R}\) 中。通过定义适当的 K 泛函，我们证明了它们的直接不等式。