坐标型单调算子系统的不动点问题及其应用
The fixed point problem for systems of coordinate-wise monotone operators and applications
摘要：
我们研究了一个多元算子系统的不动点问题，该系统是坐标单调的（即，非递减或非递增的每一个变量，独立），在设置准有序集。我们证明了这个问题等价于一个可以显式构造的混合单调算子的不动点问题。在半序度量空间中，得到了问题解的存在唯一性的一个判别准则。为了验证我们的结果，我们提供了一个应用程序的一阶微分系统的周期边值条件。从我们的论文得出的一个直接结论是，关于三重、四重或多维不动点的所有单独的最新发展都只是一个单一的、统一的和简单得多的方法的特定方面。
英文摘要：
We study the fixed point problem for a system of multivariate operators that are coordinate-wise monotone (i.e., nondecreasing or nonincreasing in each of the variables, independently), in the setting of quasi-ordered sets. We show that this problem is equivalent to the fixed point problem for a mixed monotone operator that can be explicitly constructed. As a consequence, we obtain a criterion for the existence and uniqueness of solution to our problem, in the setting of partially ordered metric spaces. To validate our results, we provide an application to a first-order differential system with periodic boundary value conditions. A direct consequence that follows from our paper is that all the separate recent developments on the subject of tripled, quadrupled or multidimensional fixed points are but particular aspects of a single, unified and much simpler approach.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
