Mittelwertungleichungen für Lösungen gewisser Differenzengleichungen. (Mean value inequalities for solutions of certain difference equations)
type: Item
instance of: scholarly article
title: Mittelwertungleichungen für Lösungen gewisser Differenzengleichungen. (Mean value inequalities for solutions of certain difference equations)
zbMATH Open document ID: 0705.39002
DOI: 10.1007/BF01833151
author: Lutz G. Lucht
published in: Aequationes Mathematicae
publication date: 1990-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/137352
review text: Let n be a positive integer and let \(a_ 1,...,a_ n\) be positive reals with \(a_ 1+...+a_ n=1\). Sufficient conditions on \(x_ 1,...,x_ n\) are given which guarantee that \(\Gamma (x_ 1^{a_ 1}\cdot...\cdot x_ n^{a_ n})\leq \Gamma^{a_ 1}(x_ 1)\cdot...\cdot \Gamma^{a_ n}(x_ n)\) (or \(\Gamma (x_ 1^{a_ 1}\cdot...\cdot x_ n^{a_ n})\geq \Gamma^{a_ 1}(x_ 1)\cdot...\cdot \Gamma^{a_ n}(x_ n),\) respectively). Moreover, for convex solutions of difference equations of the form \(f(x+1)-f(x)=\phi (x)\) \((x>0)\) for certain functions \(\phi\) the inequality \(a_ 1f(x_ 1)+...+a_ nf(x_ n)\geq f(x_ 1^{a_ 1}\cdot...\cdot x_ n^{a_ n})\) is proved under certain assumptions on \(x_ 1,...,x_ n\).
Mathematics Subject Classification ID: 39A10
Mathematics Subject Classification ID: 26D20
zbMATH DE Number: 4157161
zbMATH Keywords: mean value inequalities
zbMATH Keywords: convex solutions
zbMATH Keywords: difference equations
zbMATH Keywords: inequality
reviewed by: Helmut Länger
MaRDI profile type: Publication
cites work: Q5520081
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cites work: Bemerkungen zur Differenzengleichung g (x + 1) − g(x) = φ (x). Helmut Hasse zum 50. Geburtstag
description: scientific article; zbMATH DE number 4157161