On preserving the limit points of corresponding objects

Suppose that, for two given sequences {an} and {bn},lim infn→∞bnan=1 and let a function f be given. What can then be said about the limit behavior of the corresponding ratiof(bn)f(an) as n→∞? In general, no definite answer can be given to this question. We study a case where a definite answer is pos...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2020-06, Vol.486 (2), p.123916, Article 123916
Main Authors: Klesov, O.I., Steinebach, J.G.
Format: Article
Language:English
Subjects:
Corresponding objects
Functions preserving the asymptotic equivalence
Regularly varying functions
Set of limit points
Slowly varying functions
Citations: Items that this one cites
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Summary:Suppose that, for two given sequences {an} and {bn},lim infn→∞bnan=1 and let a function f be given. What can then be said about the limit behavior of the corresponding ratiof(bn)f(an) as n→∞? In general, no definite answer can be given to this question. We study a case where a definite answer is possible, namely the case of a regularly varying function f of nonzero order.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2020.123916