Shape-preserving approximation by polynomials

Abstract 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.

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