### Abstract

In this paper we investigate continuity properties of functions (Formula presented.) that satisfy the (p, q)-Jensen convexity inequality(Formula presented.)where H_{p} stands for the pth power (or Hölder) mean. One of the main results shows that there exist discontinuous multiplicative functions that are (p, p)-Jensen convex for all positive rational numbers p. A counterpart of this result states that if f is (p, p)-Jensen convex for all (Formula presented.), where P is a set of positive Lebesgue measure, then f must be continuous.

Original language | English |
---|---|

Pages (from-to) | 161-167 |

Number of pages | 7 |

Journal | Aequationes Mathematicae |

Volume | 89 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2015 |

### Fingerprint

### Keywords

- 26D15
- Primary 39B62
- Secondary 26D07

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics
- Discrete Mathematics and Combinatorics

### Cite this

*Aequationes Mathematicae*,

*89*(1), 161-167. https://doi.org/10.1007/s00010-014-0281-7

**Convexity with respect to families of means.** / Maksa, Gyula; Páles, Z.

Research output: Contribution to journal › Article

*Aequationes Mathematicae*, vol. 89, no. 1, pp. 161-167. https://doi.org/10.1007/s00010-014-0281-7

}

TY - JOUR

T1 - Convexity with respect to families of means

AU - Maksa, Gyula

AU - Páles, Z.

PY - 2015

Y1 - 2015

N2 - In this paper we investigate continuity properties of functions (Formula presented.) that satisfy the (p, q)-Jensen convexity inequality(Formula presented.)where Hp stands for the pth power (or Hölder) mean. One of the main results shows that there exist discontinuous multiplicative functions that are (p, p)-Jensen convex for all positive rational numbers p. A counterpart of this result states that if f is (p, p)-Jensen convex for all (Formula presented.), where P is a set of positive Lebesgue measure, then f must be continuous.

AB - In this paper we investigate continuity properties of functions (Formula presented.) that satisfy the (p, q)-Jensen convexity inequality(Formula presented.)where Hp stands for the pth power (or Hölder) mean. One of the main results shows that there exist discontinuous multiplicative functions that are (p, p)-Jensen convex for all positive rational numbers p. A counterpart of this result states that if f is (p, p)-Jensen convex for all (Formula presented.), where P is a set of positive Lebesgue measure, then f must be continuous.

KW - 26D15

KW - Primary 39B62

KW - Secondary 26D07

UR - http://www.scopus.com/inward/record.url?scp=84939872130&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84939872130&partnerID=8YFLogxK

U2 - 10.1007/s00010-014-0281-7

DO - 10.1007/s00010-014-0281-7

M3 - Article

VL - 89

SP - 161

EP - 167

JO - Aequationes Mathematicae

JF - Aequationes Mathematicae

SN - 0001-9054

IS - 1

ER -