{
  "id": "1901.06255",
  "version": "v1",
  "published": "2019-01-07T00:30:33.000Z",
  "updated": "2019-01-07T00:30:33.000Z",
  "title": "A note on $h$-convex functions",
  "authors": [
    "M. W. Alomari"
  ],
  "comment": "9 pages. arXiv admin note: text overlap with arXiv:1710.03418",
  "categories": [
    "math.CA"
  ],
  "abstract": "In this work, we discuss the continuity of $h$-convex functions by introducing the concepts of $h$-convex curves ($h$-cord). Geometric interpretation of $h$-convexity is given. The fact that for a $h$-continuous function $f$, is being $h$-convex if and only if is $h$-midconvex is proved. Generally, we prove that if $f$ is $h$-convex then $f$ is $h$-continuous. A discussion regarding derivative characterization of $h$-convexity is also proposed.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-01-07T00:30:33.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26A15",
      "26A16",
      "26A51"
    ],
    "keywords": [
      "convex functions",
      "convex curves",
      "geometric interpretation",
      "discussion regarding derivative characterization",
      "continuity"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}