On \((\alpha, a)\)-convex functions
type: Item
instance of: scholarly article
title: On \((\alpha, a)\)-convex functions
zbMATH Open document ID: 0813.26004
DOI: 10.1007/BF01196632
author: Janusz Matkowski
author: Marek Pycia
published in: Archiv der Mathematik
publication date: 1995-04-03T00:00:00Z
review text: Let \(I\subseteq \mathbb{R}\) be an open interval and \(\alpha, a\in (0,1)\) arbitrarily fixed. Under these conditions we show that there exists a nonconstant function \(f: I\to \mathbb{R}\) such that \[ f(\alpha s+ (1- \alpha) t)\leq af(s)+ (1- a) f(t),\qquad s,t\in I, \] if, and only if, the numbers \(\alpha\) and \(a\) are algebraically conjugate. This gives an answer to a question posed by N. Kuhn. Some corollaries for functions defined on convex and core open subsets of a linear space are also given.
Mathematics Subject Classification ID: 26A51
Mathematics Subject Classification ID: 26B25
Mathematics Subject Classification ID: 39B72
zbMATH DE Number: 734506
zbMATH Keywords: Jensen convex functions
zbMATH Keywords: \((\alpha,a)\)-convex functions
zbMATH Keywords: algebraically conjugate numbers
zbMATH Keywords: linear space
zbMATH Keywords: additive functions
zbMATH Keywords: supporting affine function
zbMATH Keywords: theorem of Rodé
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01196632
OpenAlex ID: W2073930464
description: scientific article; zbMATH DE number 734506