The Properties of compact-valued continuous relations on TVS-cone metric spaces

The purpose of this paper is to investigate of the properties for compact-valued contimious relation on TVS-cone metric spaces. We uses cones of topological vector spaces instead of cones of Banach spaces. It is proved that if ∫ be a lower semicontinuous relation on a metric space (X,d), then ∫(A) ⊂ f(A) for every subset A of X and fn is a compact-valued continuous relation for each n ∈ N if ∫ is a compact-valued con­- tinuous relation on a locally compact metric space (X,d). These results generalizes domains of compact-valued continuous relations from met­ ric spaces to compact-valued continuous relations from TVS-cone metric spaces.