Herein, the aim is to further investigate the properties of the generalized Picard operators introduced in Agratini et al. (Positivity 3(21):1189–1199, 2017). The motivation is based on with the purpose of furnishing appropriate positive approximation processes in the setting of large classes of exponential weighted Lp spaces via different type theorems. For this propose, firstly we give the boundness of the operators, acting from an exponential weighted \(L_{p}\) space into itself. Also, using an exponential weighted modulus of continuity a quantitative type theorem as well as the global smoothness property of the operators are presented. Then, we give pointwise approximation property of the operators at a generalized Lebesgue point. Finally under a certain condition, again the weighted Lp approximation is formulated without using Korovkin type theorem.

中文翻译：

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修改的Picard运算符的加权近似

在此，目的是进一步研究Agratini等人中引入的广义Picard算子的性质。（正值3（21）：1189-1199，2017年）。动机基于以下目的：通过不同类型的定理，在设置大类别的指数加权Lp空间时，提供适当的正逼近过程。对于此建议，首先我们根据指数加权\（L_ {p} \）给出算子的界空间本身。同样，使用指数加权连续性模量，给出了一个定量类型定理以及算子的整体光滑性。然后，我们给出了广义Lebesgue点上算子的逐点逼近性质。最终，在一定条件下，无需使用Korovkin型定理即可再次确定加权Lp逼近。