{
  "id": "2501.07613",
  "version": "v1",
  "published": "2025-01-13T09:08:37.000Z",
  "updated": "2025-01-13T09:08:37.000Z",
  "title": "A general form of Newton-Maclaurin type inequalities",
  "authors": [
    "Changyu Ren"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "In this paper, we extend the classical Newton-Maclaurin inequalities to functions $S_{k;s}(x)=E_k(x)+\\dsum_{i=1}^s \\al_i E_{k-i}(x)$, which are formed by linear combinations of multiple basic symmetric mean. We proved that when the coefficients $\\al_1,\\al_2,\\cdots,\\al_s$ satisfy the condition that the polynomial $$t^s+\\al_1 t^{s-1}+\\al_2 t^{s-2}+\\cdots+\\al_s $$ has only real roots, the Newton-Maclaurin type inequalities hold for $S_{k;s}(x)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2025-01-13T09:08:37.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "general form",
      "newton-maclaurin type inequalities hold",
      "multiple basic symmetric mean",
      "real roots",
      "linear combinations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}