论文标题
最终的集合家庭的限制，并应用于算法的公共固定点问题
Limits of eventual families of sets with application to algorithms for the common fixed point problem
论文作者
论文摘要
我们提出了一个抽象框架，用于基于我们定义的最终群体的概念，用于收敛性分析。如果在包容性方面是遗传性的，则在这里被称为“最终家庭”。我们在豪斯多夫拓扑空间中定义了最终家庭的积累点，并定义了最终家庭的“图像家族”。专注于整数中最终的家庭，使我们能够谈论要点的序列。我们将工作扩展到“多式”的概念，这是对集合概念的修改，该概念允许其元素的多个实例，并能够开发“多族”，这些“多族”要么“增加”或“减少”。此处创建的抽象结构是由我们探讨了对迭代过程的融合分析，以渐近地找到运营商家族的共同固定点。
We present an abstract framework for asymptotic analysis of convergence based on the notions of eventual families of sets that we define. A family of subsets of a given set is called here an "eventual family" if it is upper hereditary with respect to inclusion. We define accumulation points of eventual families in a Hausdorff Topological space and define the "image family" of an eventual family. Focusing on eventual families in the set of the integers enables us to talk about sequences of points. We expand our work to the notion of a "multiset" which is a modification of the concept of a set that allows for multiple instances of its elements and enable the development of "multifamilies" which are either "increasing" or "decreasing". The abstract structure created here is motivated by, and feeds back to, our look at the convergence analysis of an iterative process for asymptotically finding a common fixed point of a family of operators.
