In this research article, we construct a new sequence of Baskakov–Stancu–Durrmeyer operators including the shape parameter \(\alpha\) and study the uniform convergence of these operators by means of modulus of continuity to the continuous functions h(u) on \(u\in [0,1]\). We investigate the pointwise and weighted approximation in terms of Ditzian–Totik uniform with the aid of first and second order of modulus of smoothness. Further, we calculate the direct estimate of rate of convergence in terms of Lipschitz function. Next, we study weight approximation result.

中文翻译：

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基于形状参数-$$ \ alpha $$α的修饰的Baskakov–Durrmeyer算子的逼近性质

在本文中，我们构造了包括形状参数\（\ alpha \）的Baskakov–Stancu–Durrmeyer算子的新序列，并通过对连续函数h（u）的连续模量研究了这些算子的均匀收敛性。\（u [in [0,1] \）。我们借助一阶和二阶平滑模量研究Ditzian-Totik均匀性的逐点加权加权。此外，我们根据Lipschitz函数计算收敛速度的直接估计。接下来，我们研究权重近似结果。