Dual Cones, Constrained n-Convex Lp-Approximation, and Perfect Splines Original Research Article

A generating basis and the dual cone of n-convex functions satisfying certain constraints are derived. As applications, the existence and characterization of a best Lp-approximation (1 ≤ p < ∞) from such subcones to a function in Lp are established. The relationship between a best L1-approximation and perfect splines is developed under certain conditions.