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.
@article{bwmeta1.element.bwnjournal-article-smv120i1p75bwm,
author = {Szymon W\k asowicz},
title = {Polynomial selections and separation by polynomials},
journal = {Studia Mathematica},
volume = {119},
year = {1996},
pages = {75-82},
zbl = {0887.26007},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv120i1p75bwm}
}
Wąsowicz, Szymon. Polynomial selections and separation by polynomials. Studia Mathematica, Tome 119 (1996) pp. 75-82. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv120i1p75bwm/
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