Some comments on the paper "O jednom O-inverznom stavu" by Vojislav G. Avakumović
DOI:
https://doi.org/10.20535/mmtu-2018.1-005Keywords:
Regularly varying functions, ORV-functions, Non-degenerate group of regular points, Preserving the asymptotic equivalence.Abstract
Some comments concerning the origin of the (R–O) notion for real functions are given, which has been used in the paper above, but was first introduced by Avakumović (1935). Moreover, some later extensions and generalizations of such functions are briefly discussed.References
Aljančić, S., & Aranđelović, D. (1977). O-regularly varying functions. Publications de l’Institut mathematique, 22 (42), 5–22. http://elib.mi.sanu.ac.rs/files/journals/publ/42/1.pdf
Avakumović, V. G. (1935). Sur une extension de la condition de convergence des théoremes inverses de sommabilité. C. R. Acad. Sci. Paris, 200 , 1515–1517. https://gallica.bnf.fr/ark:/12148/bpt6k3152t
Avakumović, V. G. (1936a). O jednom O-inverznom stavu. Rad Jugoslovenske Akademije Znatnosti i Umjetnosti (Rareda Matematičko–Prirodoslovnogo), 254 (79), 167–186. https://dizbi.hazu.hr/a/?pr=iiif.v.a&id=18587
Avakumović, V. G. (1936b). Über einer O-Inversionssatz. Bull. Int. Acad. Youg. Sci., 29–30 , 107–117.
Bari, N. K., & Stechkin, S. B. (1956). Best approximations and differential properties of two conjugate functions [in Russian]. Trudy Moskovskogo Matematicheskogo Obshchestva, 5 , 483–522. http://mi.mathnet.ru/mmo56
Bingham, N. H., Goldie, C. M., & Teugels, J. L. (1989). Regular variation (Vol. 27). Cambridge: Cambridge university press.
Bojanic, R., & Seneta, E. (1971). Slowly varying functions and asymptotic relations. Journal of Mathematical Analysis and Applications, 34 (2), 302–315. https://doi.org/10.1016/0022-247X(71)90114-4
Buldygin, V. V., Indlekofer, K.-H., Klesov, O. I., & Steinebach, J. G. (2018). Pseudo regularly varying functions and generalized renewal processes. Berlin: Springer.
Buldygin, V. V., Klesov, O. I., & Steinebach, J. G. (2002). Properties of a subclass of Avakumović functions and their generalized inverses. Ukrainian Mathematical Journal, 54 (2), 179–206. https://doi.org/10.1023/A:1020178327423
Buldygin, V. V., Klesov, O. I., & Steinebach, J. G. (2004). On factorization representations for Avakumović–Karamata functions with nondegenerate groups of regular points. Analysis Mathematica, 30 (3), 161–192. https://doi.org/10.1023/B:ANAM.0000043309.79359.cc
Cline, D. B. H. (1994). Intermediate regular and Π variation. Proceedings of the London Mathematical Society, 3 (3), 594–616. https://doi.org/10.1112/plms/s3-68.3.594
Drasin, D., & Seneta, E. (1986). A generalization of slowly varying functions. Proceedings of the American Mathematical Society, 96 (3), 470–472. https://doi.org/10.2307/2046597
Feller, W. (1969). One-sided analogues of Karamata’s regular variation. L’Enseignement Math, 15, 107–121. https://doi.org/10.5169/seals-43209
Karamata, J. (1936). Bemerkung über die vorstehende Arbeit des Herrn Avakumović, mit näherer Betrachtung einer Klasse von Funktionen, welche bei den Inversionssätzen vorkommen. Bull. Int. Acad. Youg. Sci, 29–30 , 117–123.
Krasnosel’skii, M. A., & Rutickii, Y. B. (1961). Convex functions and Orlicz spaces. Groningen: P. Noordhoff.
Matuszewska, W. (1962). Regularly increasing functions in connection with the theory of ${{L}^{*varphi }}$-spaces. Studia Mathematica, 21 (3), 317–344. https://doi.org/10.4064/sm-21-3-317-344
Matuszewska, W. (1965). A remark on my paper "Regularly increasing functions in connection with the theory of ${{L}^{*varphi }}$-spaces". Studia Mathematica, 25, 265–269. https://doi.org/10.4064/sm-25-2-265-269
Seneta, E. (1976). Regularly varying functions. Berlin: Springer-Verlag.
Downloads
Issue
Section
License
Copyright (c) 2018 Mathematics in Modern Technical University
This work is licensed under a Creative Commons Attribution 4.0 International License.