THE DAMASCUS INEQUALITY

Journal Title: Проблемы анализа-Issues of Analysis - Year 2016, Vol 5, Issue 2

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.

Authors and Affiliations

F. M. Dannan, S. M. Sitnik

Keywords

Related Articles

ON THE INEQUALITIES FOR THE VOLUME OF THE UNIT BALL Ω_N IN R^N

The inequalities about the volume of the unit ball Ω_n in R^n were studies by several authors, especially Horst Alzer has a great contribution to this topic. Thereafter many authors produced numerous papers on this topic...

REDUCED p-MODULUS, p-HARMONIC RADIUS AND p-HARMONIC GREEN’S MAPPINGS

We consider the definitions and properties of the metric characteristics of the spatial domains previously introduced by the author, and their connection with the class of mappings, the particular case of which are the h...

ON THE SCHWARZIAN NORM OF HARMONIC MAPPINGS

We obtain estimations of the pre-Schwarzian and Schwarzian derivatives in terms of the order of family in linear and affine invariant families L of sense preserving harmonic mappings of the unit disk D. As the converse r...

Growth theorems on classes of normalized locally quasiconformal mappings

В классах локально-квазиконформных нормированных автоморфизмов f единичного круга Δ с заданной мажорантой характеристики М. А. Лаврентьева получены асимптотически точные оценки |f(z)|, родственные классическому неравенст...

STRUCTURE OF KELLER MAPPINGS, TWO-DIMENSIONAL CASE

A Keller map is a polynomial mapping ƒ : Rⁿ → Rⁿ (or Cⁿ → Cⁿ) with the Jacobian Jƒ ≡ const ≠ 0. The Jacobian conjecture was first formulated by O. N. Keller in 1939. In the modern form it supposes injectivity of a Keller...

Download PDF file
  • EP ID EP225106
  • DOI 10.15393/j3.art.2016.3350
  • Views 121
  • Downloads 0

How To Cite

F. M. Dannan, S. M. Sitnik (2016). THE DAMASCUS INEQUALITY. Проблемы анализа-Issues of Analysis, 5(2), 3-19. https://europub.co.uk/articles/-A-225106