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Estimates for spline projections

J. H. Bramble, A. H. Schatz (1976)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

Extending n-convex functions

Allan Pinkus, Dan Wulbert (2005)

Studia Mathematica

We are given data α₁,..., αₘ and a set of points E = x₁,...,xₘ. We address the question of conditions ensuring the existence of a function f satisfying the interpolation conditions f ( x i ) = α i , i = 1,...,m, that is also n-convex on a set properly containing E. We consider both one-point extensions of E, and extensions to all of ℝ. We also determine bounds on the n-convex functions satisfying the above interpolation conditions.

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