Topological Structures?Fixed Points And Optimization Problems On Partially Ordered Spaces

In this paper,we study topological structures,optimization and fixed points prob lems.More specially,Partially ordered spaces refers to cone b metric spaces and par tially ordered topological vector spaces in this paper.Topological structures.Let(X,d.K)be a cone b metric space over a ordered Ba nach space(E,?)with respect to cone P.We introduce a b metric pc and we prove that the b metric space induced by b metric pc has the same topological structures with the cone b metric space.Fixed Points.Ciric introduced the concept of quasi contraction and obtained a well known fixed point theorem in the setting of metric spaces.Then Ciric's result has been extended in many directions.It is worth mentioning that P.D.Proinov studied a quasi contraction type mapping and solved a open problem,M.Cvetkovic researched quasi contraction of Perov type and got some important results concerning linear operators.We study several more general quasi contraction type mappings in the framework of cone b metric spaces and obtain some results which involves coincidence points and common fixed points.Optimization.We investigate a scalarizing function's continuity and convexity un der K conditions.Utilizing that function,we convert set valued optimization problems into equilibrium problems,and then study existence of efficient solutions of set valued optimization problems with constraints,the upper semicontinuity and lower semiconti nuity of strongly approximate solution mappings to the parametric set valued optimiza tion problems.In this paper,we generalize,improve and unity many related results.