Fixed points of mappings on ordered sets (Q1703315)

The author deals with fixed points of multi-valued mappings on ordered sets, as a continuation of recent joint work with T. N. Fomenko. Sufficient conditions are given for the existence of a least element in the common fixed point set of a concordantly (chain) isotone family of multi-valued mappings on an ordered set. The problem of finding a common fixed point of a finite family of multi-valued mappings with an iterative method is considered. In addition, it is shown that under certain conditions the fixed point property is invariant under an order-homotopy connecting a pair of isotone single-valued mappings on an ordered set.