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Asymptotic similarity relation and generalized inverse

Đurčić Dragan (Technical faculty, Čačak)
Konjokrad Valentina (University of East Sarajevo, Faculty of Philosophy, Pale, Bosnia and Herzegovina)
Nikolić Rale M. (Faculty of Mathematics, Belgrade)

In this paper we discuss relationships among asymptotic similarity, weak asymptotic equivalence and the generalized inverse in the class A of all nondecreasing unbounded positive functions on a half-axis [a, +∞) (a > 0). As a main result, we prove proper characterizations of some classes of functions in Karamata’s theory of regular and rapid variation.

Keywords: regular variation, generalized inverse, relation of asymptotic similarity