{
  "id": "1712.07731",
  "version": "v1",
  "published": "2017-12-20T22:18:14.000Z",
  "updated": "2017-12-20T22:18:14.000Z",
  "title": "Some inequalities for operator (p,h)-convex functions",
  "authors": [
    "Trung Hoa Dinh",
    "Khue TB Vo"
  ],
  "journal": "Linear and Multilinear Algebra, 2017",
  "doi": "10.1080/03081087.2017.1307914",
  "categories": [
    "math.FA"
  ],
  "abstract": "Let $p$ be a positive number and $h$ a function on $\\mathbb{R}^+$ satisfying $h(xy) \\ge h(x) h(y)$ for any $x, y \\in \\mathbb{R}^+$. A non-negative continuous function $f$ on $K (\\subset \\mathbb{R}^+)$ is said to be {\\it operator $(p,h)$-convex} if \\begin{equation*}\\label{def} f ([\\alpha A^p + (1-\\alpha)B^p]^{1/p}) \\leq h(\\alpha)f(A) +h(1-\\alpha)f(B) \\end{equation*} holds for all positive semidefinite matrices $A, B$ of order $n$ with spectra in $K$, and for any $\\alpha \\in (0,1)$. In this paper, we study properties of operator $(p,h)$-convex functions and prove the Jensen, Hansen-Pedersen type inequalities for them. We also give some equivalent conditions for a function to become an operator $(p,h)$-convex. In applications, we obtain Choi-Davis-Jensen type inequality for operator $(p,h)$-convex functions and a relation between operator $(p,h)$-convex functions with operator monotone functions.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-20T22:18:14.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "convex functions",
      "operator monotone functions",
      "hansen-pedersen type inequalities",
      "choi-davis-jensen type inequality",
      "positive semidefinite matrices"
    ],
    "tags": [
      "journal article"
    ],
    "publication": {
      "publisher": "Taylor-Francis"
    },
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}