On preserving the limit points of corresponding objects

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:486

Article

Klesov, O. I.¹  Steinebach, J. G.² 

[1] Natl Tech Univ Ukraine, Igor Sikorsky Kyiv Polytech Inst, Dept Math Anal & Probabil Theory, Peremogy Ave 37, UA-03056 Kiev, Ukraine

[2] Univ Cologne, Dept Math Informat, Weyertal 86-90, D-50931 Cologne, Germany

关键词: Regularly varying functions;    Slowly varying functions;    Functions preserving the asymptotic equivalence;    Corresponding objects;    Set of limit points;   

DOI  :  10.1016/j.jmaa.2020.123916

来源: Elsevier

【 摘 要 】

Suppose that, for two given sequences {a(n)} and {b(n)}, lim inf(n ->infinity) b(n)/a(n) = 1 and let a function f be given. What can then be said about the limit behavior of the corresponding ratio f(b(n))/f(a(n)) as n -> infinity ? 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. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free