### Abstract

We consider the functional inequality (equation presented) where f is a real valued function on a linear space X. This inequality is satisfied by Jensen functions (that are solutions of the Jensen functional equation) and, in the case X = ℝ, by monotone functions. The main result of the paper shows that, under some regularity assumptions, any solution of (*) is of the form f = g o α, where α : X → ℝ is an additive function and g : ℝ → ℝ is monotone.

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

Pages (from-to) | 575-595 |

Number of pages | 21 |

Journal | Publicationes Mathematicae |

Volume | 52 |

Issue number | 3-4 |

Publication status | Published - 1998 |

### Fingerprint

### Keywords

- ℚ-quasiaffine function
- Jensen function
- Midpoint-convex and ℚ-convex set
- Midpoint-quasiaffine function

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Publicationes Mathematicae*,

*52*(3-4), 575-595.

**A characterization of midpoint-quasiaffine functions.** / Nikodem, Kazimierz; Páles, Z.

Research output: Contribution to journal › Article

*Publicationes Mathematicae*, vol. 52, no. 3-4, pp. 575-595.

}

TY - JOUR

T1 - A characterization of midpoint-quasiaffine functions

AU - Nikodem, Kazimierz

AU - Páles, Z.

PY - 1998

Y1 - 1998

N2 - We consider the functional inequality (equation presented) where f is a real valued function on a linear space X. This inequality is satisfied by Jensen functions (that are solutions of the Jensen functional equation) and, in the case X = ℝ, by monotone functions. The main result of the paper shows that, under some regularity assumptions, any solution of (*) is of the form f = g o α, where α : X → ℝ is an additive function and g : ℝ → ℝ is monotone.

AB - We consider the functional inequality (equation presented) where f is a real valued function on a linear space X. This inequality is satisfied by Jensen functions (that are solutions of the Jensen functional equation) and, in the case X = ℝ, by monotone functions. The main result of the paper shows that, under some regularity assumptions, any solution of (*) is of the form f = g o α, where α : X → ℝ is an additive function and g : ℝ → ℝ is monotone.

KW - ℚ-quasiaffine function

KW - Jensen function

KW - Midpoint-convex and ℚ-convex set

KW - Midpoint-quasiaffine function

UR - http://www.scopus.com/inward/record.url?scp=0346367710&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0346367710&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0346367710

VL - 52

SP - 575

EP - 595

JO - Publicationes Mathematicae

JF - Publicationes Mathematicae

SN - 0033-3883

IS - 3-4

ER -