... Publishing CorporationJournal of Inequalities and ApplicationsVolume 2010, Article ID 543061, 17 pagesdoi:10.1155/2010/543061 Research Article Solvability Criteria for Some Set-ValuedInequality ... Applied Mathematics, John Wiley &Sons, New York, NY, USA, 1984.10 J P. Aubin, Mathematical Methods of Game and Economic Theory, vol. 7 of Studies in Mathematics and ItsApplications, North-Holland, ... one claims that the minimaxequality of ϕ holds. Denoting by vϕ the value of the preceding equality,one also says that the minimax value vϕ of ϕ exists. If p, x ∈ P × Xsuch that supx∈Xϕp,...