The Damascus Inequality
- 07 Nov 2017
- Published Resarch - Mathematics
| Author | F. M. Dannan , F. M. Sitnik |
| Published in | Journal Problemy Analiza . Issues of Analysis. Vol. 5 (23) , No. 2 , 2016, pp. 3–19 |
| Abstract | : 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. Key words: cycle inequalities, Lagrange method, geometric inequalities, symmetric reduction. 2010 Mathematical Subject Classification: 26D15
|
| Link to read full paper |
