Geodesic
The Damascus inequality
Problemy analiza, Tome 5 (2016) no. 2, pp. 3-19 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

In 2016 Prof. Fozi M. Dannan from Damascus, Syria, proposed an interesting inequality for three positive numbers with unit product. It became widely known but was not proved yet in spite of elementary formulation. In this paper we prove this inequality together with similar ones, its proof occurred to be rather complicated. We propose some proofs based on different ideas: Lagrange multipliers method, geometrical considerations, Klamkin-type inequalities for symmetric functions, usage of symmetric reduction functions of computer packages. Also some corollaries and generalizations are considered, they include cycle inequalities, triangle geometric inequalities, inequalities for arbitrary number of values and special forms of restrictions on numbers, applications to cubic equations and symmetric functions.
Keywords: cycle inequalities; Lagrange method; geometric inequalities; symmetric reduction. 
@article{PA_2016_5_2_a0,
     author = {F. M. Dannan and S. M. Sitnik},
     title = {The {Damascus} inequality},
     journal = {Problemy analiza},
     pages = {3--19},
     year = {2016},
     volume = {5},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PA_2016_5_2_a0/}
}
TY  - JOUR
AU  - F. M. Dannan
AU  - S. M. Sitnik
TI  - The Damascus inequality
JO  - Problemy analiza
PY  - 2016
SP  - 3
EP  - 19
VL  - 5
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/PA_2016_5_2_a0/
LA  - en
ID  - PA_2016_5_2_a0
ER  - 
%0 Journal Article
%A F. M. Dannan
%A S. M. Sitnik
%T The Damascus inequality
%J Problemy analiza
%D 2016
%P 3-19
%V 5
%N 2
%U http://geodesic.mathdoc.fr/item/PA_2016_5_2_a0/
%G en
%F PA_2016_5_2_a0
F. M. Dannan; S. M. Sitnik. The Damascus inequality. Problemy analiza, Tome 5 (2016) no. 2, pp. 3-19. http://geodesic.mathdoc.fr/item/PA_2016_5_2_a0/

[1] Mitrinović D. S., Pečarić J., Fink A. M., Classical and New Inequalities in Analysis, Springer, 1993

[2] Mitrinović D. S., Vasić P. M., Analytic Inequalities, Springer, 1970 | MR | Zbl

[3] Marshall A. W., Olkin I., Arnold B. C., Inequalities: Theory of Majorization and Its Applications, Second Edition, Springer, 2011 | MR | Zbl

[4] Mitrinović D. S., Pečarić J., Volenec V., Recent Advances in Geometric Inequalities, Kluwer, 1989 | Zbl

[5] Soltman V. P., Meidman S. I., Equalities and Inequalities in a Triangle, Štiinća Publishing, Kišinev, 1982 (in Russian)

[6] Bottema O., Djordjević R.Ž., Janić R. R., Mitrinović D. S., Vasić P. M., Geometric Inequalities, Groningen, 1969 | MR