Lopez, Contractive mapping theorems in

partially ordered sets and applications to ordinary differential equations, Order, 22 (2005), 223-239.

Let (X, [less than or equal to]) be a

partially ordered set and d be a metric on X such that (X, d) is complete.

However all the vertices are real and it is a

partially ordered set.

That is, there is no order of succession implied by the space as in the

partially ordered sets and grammars.

An ordered pair <S, R> where S is a set, and R is a relation from S to S, is a

partially ordered set, if

7] Let (X, [less than or equal to]) be a

partially ordered set and let there exist a metric d in X which makes (X, d) into a complete metric space.

Hence, (R, [less than or equal to]) is a

partially ordered set.

Let A and B be two nonempty subsets of a

partially ordered set (X,[?

Let (P, [less than or equal to]) be a finite

partially ordered set (poset for short) and x, y [member of] P.

Then (G; [less than or equal to]) is a

partially ordered set and 0 is its smallest element.

be a

partially ordered set and f: X [right arrow] X and g: X [right arrow] X.

Let X be a

partially ordered set and F: X x X [right arrow] CB(X) a mapping.