Some theorems on reverse inequalities
type: Item
instance of: scholarly article
title: Some theorems on reverse inequalities
zbMATH Open document ID: 0606.26014
DOI: 10.1016/0022-247X(86)90158-7
author: Seiichi Iwamoto
author: Chung-Lie Wang
author: R. James Tomkins
published in: Journal of Mathematical Analysis and Applications
publication date: 1986-01-01T00:00:00Z
review text: This paper treats the reversion of inequalities like as arithmetic mean- geometric mean, Cauchy, Hölder, Mitrinović, Szegö, Iwamoto, and others. In particular it is shown that Cauchy and Aczél, Hölder and Popoviciu, and Minkowski and Lorentz inequalities are dual in the reverse sense. These inequalities and their reversed forms in both discrete and continuous cases are established through dynamic programming approach. Each inequality on one or two recursive function(s) with strict increasingness is reversible. The reverse inequality states a dual relation on its or their reverse function(s). Here recursive function with strict increasingness is a sequentially parametric composition of a class of strictly increasing continuous functions. Reversion is also a sequentially parametric extension of inversion.
Mathematics Subject Classification ID: 26D15
Mathematics Subject Classification ID: 90C39
Mathematics Subject Classification ID: 49L20
zbMATH DE Number: 3979421
zbMATH Keywords: reversion of inequalities
zbMATH Keywords: discrete and continuous cases
zbMATH Keywords: dynamic programming approach
zbMATH Keywords: sequentially parametric extension of inversion
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3979421