Continuous and Discrete n-Convex Approximation
Approximation Theory and its Applications
We show that the best Lp-approximant to continuous functions by n-convex functions is the limit of discrete n-convex approximations. The techniques of the proof are then used to show the existence of near interpolants to discrete n-convex data by continuous n-convex functions if the data points are close.
David A. Legg and Douglas W. Townsend (1992).
Continuous and Discrete n-Convex Approximation. Approximation Theory and its Applications.8 (4), 28-34.