On j-Convex Preserving Interpolation Operators

Abstract

We present results regarding the existence of j-convex preserving interpolation operators, as well as results concerning the determination of existence of such operators. We include an application in which we make use of a sufficient set of testfunctions to characterize when every degree of convexity can be preserved among particular families of polynomial interpolation operators, which include the Bernstein operators. Academic Press

Minimal multi-convex projections

“…When P ∈ P S we say P is shape-preserving (in the sense of S). Some basic results on the existence of shape-preserving projections can be found in [10], [31], [12] and [34]. Not surprisingly, for given X, V and S, the problem of determining if P S = ∅ is nontrivial in general.…”