# Minkowski’s inequality and sums of squares

Open Mathematics (2014)

- Volume: 12, Issue: 3, page 510-516
- ISSN: 2391-5455

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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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