关于联合不动点的逼近
On approximation of joint fixed points
摘要：
对于给定的偏序集和偏序集到自身的映射族，研究了这类映射族的联合不动点的刻画问题。著名的塔斯基定理给出了完全格上保序自同构的联合不动点的集合的结构。这个定理有几个推广（见，例如，在一个实施例中，Markowsky，Ronse），削弱了对序结构的要求，并以适当的方式提升了对联合不动点集结构的断言。然而，缺乏类似Kantorovich或Kleene定理的表述，即用算子次数的收敛序列来描述联合不动点的集合。本文给出了偏序集和族的条件，这些条件保证族中元素的迭代序列逼近联合不动点集。所得结果在构造性的方向上发展了上述关于联合不动点的定理。
英文摘要：
For a given partially ordered set (poset) and a given family of mappings of the poset into itself, we study the problem of the description of joint fixed points of this family. Well-known Tarski's theorem gives the structure of the set of joint fixed points of isotone automorphisms on a complete lattice. This theorem has several generalizations (see., e.g., Markowsky, Ronse) that weaken demands on the order structure and upgrade in an appropriate manner the assertion on the structure of the set of joint fixed points. However, there is a lack of the statements similar to Kantorovich or Kleene theorems, describing the set of joint fixed points in terms of convergent sequences of the operator degrees. The paper provids conditions on the poset and on the family; these conditions ensure that the iterative sequences of elements of this family approximate the set of joint fixed points. The result obtained develops in a constructive direction the mentioned theorems on joint fixed points.
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