We consider a family of operators which is a link between classical Baskakov operators (for ) and their genuine Durrmeyer type modification (for ). First, we prove that for fixed and a fixed convex function , is decreasing with respect to . We give two proofs, using various probabilistic considerations. Then, we combine this property with some existing direct and strong converse results for classical operators, in order to get such results for the operators applied to convex functions.

中文翻译：

---

链接运算符和凸函数的强大逆结果

我们考虑一个算子家族，它是经典Baskakov算子之间的链接（对于）及其真正的Durrmeyer类型修改（用于）。首先，我们证明和一个固定的凸函数， 相对于下降。我们使用各种概率考虑给出两个证明。然后，我们将此性质与经典算子的一些现有直接和强逆结果结合起来，以得到应用于凸函数的算子的此类结果。