BOUNDARY SOLUTIONS OF OPERATOR EQUATIONS IN PARIAL ORDERING SETS WITH APPLICATIONS TO SYSTEMS OF FUNCTIONALEQUATIONS

In this papert we study the existence of solutions and boundary solutions tothe following system of operator equations in partial ordering sets.We do not assume any topological structure or algebraic structure on the partial orderingsets. The quasi-order completeness of the ranges on Akik, Bkjk (ik = 1, 2,... mk,jk =1, 2,'' nk) is the main condition in the theorems. We discuss the quasi-order completesets in some concrete spaces. As corollaries, we obtain some new coupled fixed point resultsfor mixed monotone operators. Lastly the conclusions are applied to a system of functionalequations arising in dyntaic programming.