A concept on well ordered set is generalized to semi well ordered set,which contains positive integer ordered set,negative integer ordered set,integer ordered set,well ordered set and extensional well ordered set.

There are a variety of known ways in which a partially ordered set P may be given a convergence.

Basing on some characteristics of supremum and order convergence, a corollary of Zorn lemma is given in partially ordered set.

The existence of the minimal and maximal fixed points for order preserving set-valued operators on semi-ordered sets and semi-ordered topological spaces was analyzed.

By introducing the concepts of the totally ordered quasicomplete set and totally ordered self-complete set in this paper, some existence theorems of coupled fixed point for mixed monotone mappings in semi-ordered set and its application are given.

In this paper,some definitions of the mixed monotonicity for set-valued operators in semiordered set are introduced and relation of monotonicities are discussed.

Then using some propertis of the total ordered subset in semiordered set, the existence theorems of coupled fixed points and minimax coupled fixed points for mixed monotone set valued operators are given.

By introducing the concepts of the lower increasing,upperincreasing ,total increasing and strong increasing for set valued operators and the concepts of totally ordered quasi complete set and totally self complete set in semiordered set ,the existence of fixed point for the set valued increasing operators composed of a single valued operator and a set valued operator is discussed.

It is proved that if P is a cac poset, then D(P)=｛x∈P :there is a  maximal element y such as xy｝=P .

In this paper, the concepts of the totally ordered quasi-complete set and the totally ordered self-complete set are introduced, and the fixed point theorems of composite single-valued increasing operator in partly ordered set are given.