Geodesic
Polynomial selections and separation by polynomials
Studia Mathematica, Tome 120 (1996) no. 1, pp. 75-82

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

K. Nikodem and the present author proved in [3] a theorem concerning separation by affine functions. Our purpose is to generalize that result for polynomials. As a consequence we obtain two theorems on separation of an n-convex function from an n-concave function by a polynomial of degree at most n and a stability result of Hyers-Ulam type for polynomials.
DOI : 10.4064/sm-120-1-75-82
Keywords: separation theorem, set-valued function, selection, n-convex function, n-concave function, affine function, Helly's theorem, Lagrange interpolating polynomial

Szymon Wąsowicz 1

1 
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Szymon Wąsowicz. Polynomial selections and separation by polynomials. Studia Mathematica, Tome 120 (1996) no. 1, pp. 75-82. doi: 10.4064/sm-120-1-75-82

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