Conic systems and sublinear mappings: equivalent approaches. (Q703260)

It was previously recognized that linear conic systems \(Ax=b, x\in C\) where \(A\) is a linear mapping of real Banach spaces, \(C\) is a closed convex cone, are special cases of sublinear mappings: set-valued mappings such that \(\lambda F(x)+\mu F(y) \subset F(\lambda x +\mu y)\). The author observes the converse is also true, giving a correspondence between results on these two kinds of mappings, and applies it to the study of the distance to ill-posedness.