Some asymptotic relations for the generalized inverse

In this paper we investigate the connection between the asymptotic relations of subordination and the negligence with the generalized inverse function in the class of all nondecreasing and unbounded functions, which are defined on a half-axis [a,+∞) (a>0). In the main theorems we prove a characterization of all nondecreasing, unbounded slowly varying functions. © 2007 Elsevier Inc. All rights reserved.