On a trinomial analogue of Muirhead's inequaty

Abdulla Azamov

doi:10.29229/uzmj.2026-1-3

On a trinomial analogue of Muirhead's inequaty

Authors

Abdulla Azamov V.I.Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences Author

DOI:

https://doi.org/10.29229/uzmj.2026-1-3

Keywords:

Muirhead’s inequality, symmetric polynomial, circle division polynomial, arithmetic function

Abstract

It is studied inequalities between three elementary symmetric polynomials being trinomial generalization of the well-known Muirhead's inequality. Some sufficient conditions have been derived. A sufficient and necessary condition is given in the case of two variables.