Paper Title:

Some Homogeneous Cyclic Inequalities of Three Variables of Degree Three and Four

Author(s):

TETSUYA ANDO

Department of Mathematics and Informatics,
 Chiba University, Chiba 263-8522, JAPAN

ando@math.s.chiba-u.ac.jp

Abstract:

We shall show that the three variable cubic inequality
    t² (a³+b³+c³) + (t⁴-2t)(ab²+bc²+ca²)
            ≥ (2t³-1)(a²b+b²c+c²a) + (3t⁴-6t³+3t²-6t+3)abc
holds for non-negative a, b, c, and for any real number t.
We also show some similar three variable cyclic quartic inequalities.
 

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