On Min-Max Affine Approximants of Convex or Concave Real-Valued Functions from $$\mathbb R^k$$ , Chebyshev Equioscillation and Graphics

  title={On Min-Max Affine Approximants of Convex or Concave Real-Valued Functions from \$\$\mathbb R^k\$\$ , Chebyshev Equioscillation and Graphics},
  author={Steven Benjamin Damelin and David L. Ragozin and Michael Werman},
  journal={Applied and Numerical Harmonic Analysis},
We study Min-Max affine approximants of a continuous convex or concave function f : Δ ⊂ R − → R where Δ is a convex compact subset of R . In the case when Δ is a simplex we prove that there is a vertical translate of the supporting hyperplane in Rk+1 of the graph of f at the vertices which is the unique best affine approximant to f on Δ. For k = 1, this result provides an extension of the Chebyshev equioscillation theorem for linear approximants. Our result has interesting connections to the… 

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