Some Homogeneous Cyclic Inequalities of Three Variables of Degree Three and Four
Department of Mathematics and Informatics,
Chiba University, Chiba 263-8522, JAPAN
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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