On a generalized Minkowski inequality and its relation to dominates for t-norms
type: Item
instance of: scholarly article
title: On a generalized Minkowski inequality and its relation to dominates for t-norms
zbMATH Open document ID: 0549.26013
DOI: 10.1007/BF02192679
author: Robert M. Tardiff
published in: Aequationes Mathematicae
publication date: 1984-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/137032
review text: Der Verf. beweist u.a. den folgenden Satz: Es sei h eine für alle nichtnegativen Zahlen definierte und differenzierbare, streng wachsende konvexe Funktion, für die \(h(0)=0\) und \(h(x)\geq 0(x>0)\) gilt. Falls \(x\mapsto\log h'(e^ x)\) konvex ist, dann ist \[ h^{- 1}(h(x+y)+h(u+v))\leq h^{-1}(h(x)+h(u))+h^{-1}(h(y)+h(v)) \] für alle x,y,u,\(v\geq 0\) gültig. Daraus zieht er Folgerungen bezüglich der Relation ''dominiert'' in der Theorie der Dreiecksnormen [vgl. \textit{B. Schweizer} und \textit{A. Sklar}, Probabilistic metric spaces (1983; Zbl 0546.60010)].
Mathematics Subject Classification ID: 26D15
Mathematics Subject Classification ID: 26A51
Mathematics Subject Classification ID: 51F99
zbMATH DE Number: 3875589
zbMATH Keywords: generalized Minkowski inequality
zbMATH Keywords: dominates for strict t-norms
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3875589