A Generalization of Newton–Maclaurin’s 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. Using these inequalities, we also generalize some inequalities of Lin and Trudinger [18], which are relevant to the study of partial differential equations associated with curvature problems.