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O-Regularly Varying Functions and Strong Asymptotic Equivalence

✍ Scribed by Dragan Djurčić

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
163 KB
Volume
220
Category
Article
ISSN
0022-247X

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✦ Synopsis

In this paper we prove that in the class of all measurable positive functions w . Ž . defined on the interval a, qϱ a ) 0 , the class of functions which preserve the Ä w .

q Ž . strong asymptotic equivalence on the set of functions x: a, qϱ ¬ ‫ޒ‬ , x t ª 4 qϱ, t ª qϱ , is a class of O O-regularly varying functions with continuous index function. We also prove a representation theorem for functions from this class.

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✍ Dragan Djurčić; Aleksandar Torgašev 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 76 KB

In this paper we consider the class of functions K c introduced by W. Matuszewska (1964, Studia Math. 24, 271-279) and W. Matuszewska and W. Orlicz (1965, Studia Math. 26, 11-24). As a main result we describe, in terms of the class K c , when two strictly increasing functions, as well as their inver