### Abstract

A family F of continuous real functions defined on an interval I is a twoparameter family if for any two points (x_{1}, y_{1}), (x_{2}, y_{2}) ∈ I × ℝ with x_{1} ≠ x_{2} there exists exactly one ϕ = ϕ_{(x1,y1)(x2,y2)} ∈ F such that ϕ(x_{i}) = y_{i} for i = 1, 2. Following Beckenbach [1] a function f: I → ℝ is said to be F-convex if for any x_{1}, x_{2} ∈ I, x_{1} < x_{2} f(x) ≤ ϕ_{(x1,f (x1))(x2,f (x2))}(x), x_{1} ≤ x ≤ x_{2}. In the talk some characterization of pairs of functions that can be separated by a function belonging to F are given. As a consequence, the following sandwich theorem and a Hyers-Ulam-type stability result are obtained:.

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

Pages (from-to) | 39-40 |

Number of pages | 2 |

Journal | Real Analysis Exchange |

Volume | 32 |

Issue number | 1 |

Publication status | Published - Jan 1 2007 |

### ASJC Scopus subject areas

- Analysis
- Geometry and Topology

## Fingerprint Dive into the research topics of 'Generalized covex functions and separation theorems'. Together they form a unique fingerprint.

## Cite this

Nikodem, K., & Páles, Z. (2007). Generalized covex functions and separation theorems.

*Real Analysis Exchange*,*32*(1), 39-40.