The weak and strong asymptotic equivalence relations and the generalized inverse

The weak and strong asymptotic equivalence relations and the generalized inverse

We discuss the relationship between the weak and strong asymptotic equivalence relations and the generalized inverse in the class of all nondecreasing unbounded positive functions on a half-axis [ a, + ∞ ) ( a >  0). As a main result, we prove a proper characterization of the functional class R ∞...

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Veröffentlicht in:Lithuanian mathematical journal 2011-10, Vol.51 (4), p.472-476
Hauptverfasser: Djurčić, Dragan, Nikolić, Rale M., Torgašev, Aleksandar
Format: Artikel
Sprache:eng
Schlagworte:
Actuarial Sciences
Mathematics
Mathematics and Statistics
Number Theory
Ordinary Differential Equations
Probability Theory and Stochastic Processes
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Zusammenfassung:We discuss the relationship between the weak and strong asymptotic equivalence relations and the generalized inverse in the class of all nondecreasing unbounded positive functions on a half-axis [ a, + ∞ ) ( a >  0). As a main result, we prove a proper characterization of the functional class R ∞ ∩ , where R ∞ is the class of all rapidly varying functions. Also, we prove a characterization of the functional class PI * ∩ .
ISSN:0363-1672
1573-8825
DOI:10.1007/s10986-011-9141-5