{
  "id": "1507.05295",
  "version": "v1",
  "published": "2015-07-19T14:45:25.000Z",
  "updated": "2015-07-19T14:45:25.000Z",
  "title": "Implications between generalized convexity properties of real functions",
  "authors": [
    "Tibor Kiss",
    "Zsolt Páles"
  ],
  "categories": [
    "math.CA"
  ],
  "abstract": "Motivated by the well-known implications among $t$-convexity properties of real functions, analogous relations among the upper and lower $M$-convexity properties of real functions are established. More precisely, having an $n$-tuple $(M_1,\\dots,M_n)$ of continuous two-variable means, the notion of the descendant of these means (which is also an $n$-tuple $(N_1,\\dots,N_n)$ of two-variable means) is introduced. In particular, when all the means $M_i$ are weighted arithmetic, then the components of their descendants are also weighted arithmetic means. More general statements are obtained in terms of the generalized quasi-arithmetic or Matkowski means. The main results then state that if a function $f$ is $M_i$-convex for all $i\\in\\{1,\\dots,n\\}$, then it is also $N_i$-convex for all $i\\in\\{1,\\dots,n\\}$. Several consequences are discussed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-07-19T14:45:25.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26D15"
    ],
    "keywords": [
      "real functions",
      "generalized convexity properties",
      "two-variable means",
      "general statements",
      "descendant"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}