Shape-preserving approximation by polynomials

摘要

We are going to survey recent developments and achievements in shape-preserving approximation by polynomials. We wish to approximate a function f defined on a finite interval, say [−1,1], while preserving certain intrinsic “shape” properties. To be specific we demand that the approximation process preserves properties of f, like its sign in all or part of the interval, its monotonicity, convexity, etc. We will refer to these properties as the shape of the function.