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Sibirsk. Mat. Zh., 2008, Volume 49, Number 4, Pages 786–795 (Mi smj1877)  

This article is cited in 8 scientific papers (total in 8 papers)

The strong asymptotic equivalence and the generalized inverse

D. Djurčića, A. Torgaševb, S. Ješićc

a University of Kragujevac, Technical Faculty Cacak
b University of Belgrade, Faculty of Mathematics
c School of Electrical Engineering, University of Belgrade

Abstract: We discuss the relationship between the strong asymptotic equivalence relation and the generalized inverse in the class $\mathscr A$ of all nondecreasing and unbounded functions, defined and positive on a half-axis $[a,+\infty)$ ($a>0$). In the main theorem, we prove a proper characterization of the function class $IRV\cap\mathscr A$, where $IRV$ is the class of all $\mathscr O$-regularly varying functions (in the sense of Karamata) having continuous index function.

Keywords: regular variability, generalized inverse, asymptotic equivalence.

Full text: PDF file (336 kB)
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English version:
Siberian Mathematical Journal, 2008, 49:4, 628–636

Bibliographic databases:

UDC: 513.88
Received: 02.11.2006

Citation: D. Djurčić, A. Torgašev, S. Ješić, “The strong asymptotic equivalence and the generalized inverse”, Sibirsk. Mat. Zh., 49:4 (2008), 786–795; Siberian Math. J., 49:4 (2008), 628–636

Citation in format AMSBIB
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\paper The strong asymptotic equivalence and the generalized inverse
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\yr 2008
\vol 49
\issue 4
\pages 786--795
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\transl
\jour Siberian Math. J.
\yr 2008
\vol 49
\issue 4
\pages 628--636
\crossref{https://doi.org/10.1007/s11202-008-0059-z}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Djurčić D., Torgašev A., “A theorem of Galambos-Bojanić-Seneta type”, Abstr. Appl. Anal., 2009, 360794, 6 pp.  mathscinet  zmath  isi
    2. Djurčić D., Nikolić R., Torgašev A., “The weak asymptotic equivalence and the generalized inverse”, Lith. Math. J., 50:1 (2010), 34–42  crossref  mathscinet  zmath  isi  scopus
    3. Djurčić D., Nikolić R.M., Torgašev A., “The weak and strong asymptotic equivalence relations and the generalized inverse”, Lith. Math. J., 51:4 (2011), 472–476  crossref  mathscinet  zmath  isi  scopus
    4. Djurčić D., Mitrović I., Janjić M., “The weak and the strong equivalence relation and the asymptotic inversion”, Filomat, 25:4 (2011), 29–36  crossref  mathscinet  zmath  isi  scopus
    5. Elez N., Djurcic D., “Some Properties of Rapidly Varying Functions”, J. Math. Anal. Appl., 401:2 (2013), 888–895  crossref  mathscinet  zmath  isi  scopus
    6. Kostenko A., Teschl G., “Spectral Asymptotics for Perturbed Spherical Schrodinger Operators and Applications to Quantum Scattering”, Commun. Math. Phys., 322:1 (2013), 255–275  crossref  mathscinet  zmath  isi  elib  scopus
    7. Timotic V., Djurcic D., Nikolic R.M., “on Slowly Varying Sequences”, Filomat, 29:1 (2015), 7–12  crossref  mathscinet  zmath  isi  scopus
    8. Eckhardt J., Kostenko A., Teschl G., “Spectral Asymptotics For Canonical Systems”, J. Reine Angew. Math., 736 (2018), 285–315  crossref  mathscinet  zmath  isi  scopus
  • Сибирский математический журнал Siberian Mathematical Journal
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