Some Maximal Elements' Theorems in -Spaces

Let I be a finite or infinite index set, let X be a topological space, and let (Yi,φNi)i∈I be a family of FC-spaces. For each i∈I, let Ai:X→2Yi be a set-valued mapping. Some new existence theorems of maximal elements for a set-valued mapping and a family of set-valued mappings involving a better admissible set-valued mapping are established under noncompact setting of FC-spaces. Our results improve and generalize some recent results