Generalized covex functions and separation theorems

Kazimierz Nikodem, Zsolt Páles

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

A family F of continuous real functions defined on an interval I is a twoparameter family if for any two points (x1, y1), (x2, y2) ∈ I × ℝ with x1 ≠ x2 there exists exactly one ϕ = ϕ(x1,y1)(x2,y2) ∈ F such that ϕ(xi) = yi for i = 1, 2. Following Beckenbach [1] a function f: I → ℝ is said to be F-convex if for any x1, x2 ∈ I, x1 < x2 f(x) ≤ ϕ(x1,f (x1))(x2,f (x2))(x), x1 ≤ x ≤ x2. 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 languageEnglish
Pages (from-to)39-40
Number of pages2
JournalReal Analysis Exchange
Volume32
Issue number1
Publication statusPublished - Jan 1 2007

ASJC Scopus subject areas

  • Analysis
  • Geometry and Topology

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