Geodesic
O-regularly Varying Functions and Some Asymptotic Relations
Publications de l'Institut Mathématique, _N_S_61 (1997) no. 75, p. 44
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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 morphism-theorem for some asymptotic relations.
Classification : 26A12 
@article{PIM_1997_N_S_61_75_a6,
     author = {Dragan {\DJ}ur\v{c}i\'c},
     title = {O-regularly {Varying} {Functions} and {Some} {Asymptotic} {Relations}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {44 },
     year = {1997},
     volume = {_N_S_61},
     number = {75},
     zbl = {0901.26002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_1997_N_S_61_75_a6/}
}
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Dragan Đurčić. O-regularly Varying Functions and Some Asymptotic Relations. Publications de l'Institut Mathématique, _N_S_61 (1997) no. 75, p. 44 . http://geodesic.mathdoc.fr/item/PIM_1997_N_S_61_75_a6/