Minkowski’s inequality and sums of squares
Open Mathematics (2014)
- Volume: 12, Issue: 3, page 510-516
- ISSN: 2391-5455
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Abstract
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topPéter Frenkel, and Péter Horváth. "Minkowski’s inequality and sums of squares." Open Mathematics 12.3 (2014): 510-516. <http://eudml.org/doc/269410>.
@article{PéterFrenkel2014,
abstract = {Positive polynomials arising from Muirhead’s inequality, from classical power mean and elementary symmetric mean inequalities and from Minkowski’s inequality can be rewritten as sums of squares.},
author = {Péter Frenkel, Péter Horváth},
journal = {Open Mathematics},
keywords = {Algebraic inequalities; Minkowski’s inequality; Positive polynomials; Sums of squares; algebraic inequalities; Minkowski's inequality; positive polynomials; sums of squares},
language = {eng},
number = {3},
pages = {510-516},
title = {Minkowski’s inequality and sums of squares},
url = {http://eudml.org/doc/269410},
volume = {12},
year = {2014},
}
TY - JOUR
AU - Péter Frenkel
AU - Péter Horváth
TI - Minkowski’s inequality and sums of squares
JO - Open Mathematics
PY - 2014
VL - 12
IS - 3
SP - 510
EP - 516
AB - Positive polynomials arising from Muirhead’s inequality, from classical power mean and elementary symmetric mean inequalities and from Minkowski’s inequality can be rewritten as sums of squares.
LA - eng
KW - Algebraic inequalities; Minkowski’s inequality; Positive polynomials; Sums of squares; algebraic inequalities; Minkowski's inequality; positive polynomials; sums of squares
UR - http://eudml.org/doc/269410
ER -
References
top- [1] Caicedo A., Positive polynomials, http://caicedoteaching.wordpress.com/2008/11/11/275-positive-polynomials/
- [2] Fidalgo C., Kovacec A., Positive semidefinite diagonal minus tail forms are sums of squares, Math. Z., 2011, 269(3–4), 629–645 http://dx.doi.org/10.1007/s00209-010-0753-y[WoS][Crossref] Zbl1271.11045
- [3] Fujisawa R., Algebraic means, Proc. Imp. Acad., 1918, 1(5), 159–170 http://dx.doi.org/10.3792/pia/1195582221[Crossref]
- [4] Ghasemi M., Marshall M., Lower bounds for polynomials using geometric programming, SIAM J. Optim., 2012, 22(2), 460–473 http://dx.doi.org/10.1137/110836869[Crossref] Zbl1272.12004
- [5] Hurwitz A., Über den Vergleich des arithmetischen und des geometrischen Mittels, In: Mathematische Werke II: Zahlentheorie, Algebra und Geometrie, Birkhäuser, Basel, 1932, 505–507
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