A generalization of Newton-Maclaurin's inequalities

TL;DR

This paper extends classical Newton-Maclaurin inequalities to a broader class of functions formed by linear combinations of neighboring primary symmetry functions, enhancing the theoretical framework of inequalities in symmetric function theory.

Contribution

The paper introduces a generalized form of Newton-Maclaurin inequalities applicable to new classes of functions involving linear combinations of primary symmetry functions.

Findings

Proved generalized Newton-Maclaurin inequalities for specific function classes.

Extended the applicability of classical inequalities to broader symmetric functions.

Provided theoretical foundations for future research in symmetric function inequalities.

Abstract

In this paper, we prove Newton-Maclaurin type inequalities for functions obtained by linear combination of two neighboring primary symmetry functions, which is a generalization of the classical Newton-Maclaurin inequality.