Let A, B, C, and D be posets. Assume C and D are finite with a greatest element. Also assume that AC ≅B D. Then there exist posets E, X, Y , and Z such that A ≅E X, B ≅E Y , C≅Y ×Z, and D≅X×Z. If C≅D, then A≅B. This generalizes a theorem of Jónsson and McKenzie, who proved it when A and B were meet-semilattices.

In this paper, we introduce a new class of (semi)hypergroup from a given (Partially) quasi-ordered (semi) hypergroup as a generaliza- tion of "El-hyperstructures". Then, we study some basic properties and important elements belong to this class.

In this paper, a concept of generalized weakly contraction map-pings in Partially ordered fuzzy metric spaces is introduced and coincidence point theorems on Partially ordered fuzzy metric spaces are proved. Also, as the corollary of these theorems, some common fixed point theorems on Partially ordered fuzzy metric spaces are presented.

This paper is aimed at proving the existence of a solution to the Volterra-Hamerstain integral equations in Partially-ordered spaces. To this end, some fixed point theorems are proved in this kind of spaces.

In this paper, we prove some fixed point theorems for modular metric spaces endowed with partial order sets by using the mixed monotone mapping property which is a generalization of the definitions and results of T. Gnana Bhaskar and V. Lakshmikantham.