Interpolation and Approximation from Convex Sets Original Research Article

LetXbe a topological vector space,Y=Rn,n∈N,Abe a continuous linear map fromXtoY, C⊂X, Bbe a convex set dense inC, andd∈Ybe a data point. We derive conditions which guarantee that the setB∩A−1(d) is nonempty and dense inC∩A−1(d). Some applications to shape preserving interpolation and approximation are described.