Weak Copositive and Intertwining Approximation Original Research Article

It is known that shape preserving approximation has lower rates than unconstrained approximation. This is especially true for copositive and intertwining approximations. Forf∈Lp, 1⩽p<∞, the former only has rateωϕ(f, n−1)p, and the latter cannot even be bounded byC ‖f‖p. In this paper, we discuss various ways to relax the restrictions in these approximations and conclude that the most sensible way is the so-calledalmostcopositive/intertwining approximation in which one relaxes the restriction on the approximants in a neighborhood of radiusΔn(yj) of each sign changeyj.