Global attractivity results in partially ordered complete metric spaces

Abstract

We prove fixed point theorems for monotone mappings in partially ordered complete metric spaces which satisfy a weaker contraction condition for all points that are related by a given ordering. We also give a global attractivity result for all solutions of the difference equation $$ z_{n+1} = F(z_n, z_{n-1}), \quad n=2,3 \ldots $$ where $F$ satisfies certain monotonicity conditions with respect to the given ordering.