Functional equations on convex sets
type: Item
instance of: scholarly article
title: Functional equations on convex sets
zbMATH Open document ID: 0849.39007
DOI: 10.1007/BF01874674
author: Gyula Maksa
author: Zoltán Daróczy
published in: Acta Mathematica Hungarica
publication date: 1996-11-10T00:00:00Z
review text: Let \(X\) be a real or complex linear space and \(K \subset X\) be a convex absorbing balanced subset. The authors deal with the question under which conditions a function \(f : K \to \mathbb{C}\) has the property that for given \(\alpha \in ]0,1[\), \(\alpha \neq 1/2\), the Jensen difference \[ f \bigl( \alpha x + (1 - \alpha) y \bigr) - \alpha f(x) - (1 - \alpha) f(y) \] is symmetric in \(x\) and \(y\). In characterizing those functions they also deal with the structure of ``local'' polynomials, i.e. solutions \(g\) of the equation \[ \Delta_y^{n + 1} g(x) = 0 \] on certain subsets of \(X\).
reviewed by: Jens Schwaiger
Mathematics Subject Classification ID: 39B52
Mathematics Subject Classification ID: 39B32
Mathematics Subject Classification ID: 39A10
zbMATH DE Number: 792799
zbMATH Keywords: difference equation
zbMATH Keywords: functional equations
zbMATH Keywords: convex sets
zbMATH Keywords: local polynomials
zbMATH Keywords: linear space
zbMATH Keywords: Jensen difference
zbMATH Keywords: symmetric
MaRDI profile type: Publication
cites work: A representation theorem for $(X_1-1)(X_2-1)...(X_n-1)$ and its applications
cites work: Q3218572
cites work: Q5676645
cites work: Q5667036
cites work: Q4002300
cites work: Q3327052
cites work: Q3874718
description: scientific article; zbMATH DE number 792799