On a generalized Minkowski inequality and its relation to dominates for t-norms. (English) Zbl 0549.26013
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. B. Schweizer und A. Sklar, Probabilistic metric spaces (1983; Zbl 0546.60010)].
Reviewer: J.Aczél
MSC:
| 26D15 | Inequalities for sums, series and integrals |
| 26A51 | Convexity of real functions in one variable, generalizations |
| 51F99 | Metric geometry |
Citations:
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