In this paper, by using the partial order method, the existence and uniqueness of a solution for systems of a class of abstract operator equations in Banach spaces are discussed. The result obtained in this paper improves and unifies many recent results. Two applications to the system of nonlinear differential equations and the systems of nonlinear differential equations in Banach spaces are given, and the unique solution and interactive sequences which converge the unique solution and the error estimation are obtained.

中文翻译：

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Banach空间中一类抽象算子方程组的迭代解及其应用

本文采用偏序方法，讨论了Banach空间中一类抽象算子方程组解的存在性和唯一性。本文获得的结果改进并统一了许多最新结果。给出了在Banach空间中非线性微分方程系统和非线性微分方程系统的两个应用，并获得了唯一解和使唯一解与误差估计收敛的交互序列。