This study is a natural continuation of modified Picard operators, defined by Agratini et al, preserving an exponential function. Herein, we first show that these operators are approximation processes in the setting of large classes of weighted spaces. Then, we obtain weighted uniform convergence of the operators via exponential weighted modulus of smoothness. Finally, we give, by using the weighted modulus of continuity, the result regarding global smoothness preservation properties for the generalized Picard operators, which based in Agratini et al.

中文翻译：

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关于修改的Picard积分算子的注释

这项研究是Agratini等人定义的修饰Picard算子的自然延续，保留了指数函数。在这里，我们首先证明这些算子是大类加权空间设置中的近似过程。然后，我们通过指数加权的平滑度来获得算子的加权均匀收敛。最后，我们使用加权的连续模数，得出关于基于Agratini等人的广义Picard算子的全局光滑度保持性质的结果。