Volume 37 • Number 2 • 2014   • Approximately Midconvex Set-Valued Functions Alireza Kamel Mirmostafaee and Mostafa Mahdavi Abstract. We will show that if $F$ is a set-valued mapping which satisfies $F(x) + F(y) ⊆ 2F ((x+y)/2)+ K$ for some convex compact set $K$, then under some restrictions, there are maximal superadditive and midconvex mappings which are $K$-subclose to $F$ 2010 Mathematics Subject Classification: 39B62, 39B52, 39B82, 26B51 Full text: PDF