PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.) Vol. 61(75), pp. 4452 (1997) 

Oregularly varying functions and some asymptotic relationsDragan Djurci\'cAbstract: We prove that in the class of measurable positive functions defined on the interval $I_a = [\,a,+\infty )$ $(a > 0)$, the class of functions which preserve the strong asymptotic equivalence on the set of functions $\{x \,\colon I_a \mapsto \Bbb R^+ ,\, x(t) \to +\infty, t \to +\infty \}$, is a class of $\Cal O$regularly varying functions with continuous index function. We also prove a representation theorem for functions from this class, and a morphismtheorem for some asymptotic relations. Classification (MSC2000): 26A12 Full text of the article:
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