The \(N\)-Fixed Point Property in Posets

Abstract

In this paper, a generalized notion of the fixed point property,namely the \(n\)-fixed point property, for posets is discussed. The \(n\)-fixed point property is proved to be equivalent to the fixed point property in lattices. Further, it is shown that a poset of finite width has the \(n\)-fixed point property for some natural number \(n\) if and only if every maximal chain in it is a complete lattice.