Abstract
We discuss the relationship between the weak and strong asymptotic equivalence relations and the generalized inverse in the class \( \mathcal {A} \) 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 ∞ ∩ \( \mathcal {A} \), where R ∞ is the class of all rapidly varying functions. Also, we prove a characterization of the functional class PI * ∩ \( \mathcal {A} \).
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*Supported by the Ministry of Science of the Republic of Serbia, grant No. 174032.
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Djurčić, D., Nikolić, R.M. & Torgašev, A. The weak and strong asymptotic equivalence relations and the generalized inverse* . Lith Math J 51, 472–476 (2011). https://doi.org/10.1007/s10986-011-9141-5
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DOI: https://doi.org/10.1007/s10986-011-9141-5