A few remarks on divergent sequences: rates of divergence. II. (English) Zbl 1196.40002
In several recent papers the authors investigated relations between the theory of divergent processes in asymptotic analysis and the theory of selection principles and games. The present paper extends and improves a result (Theorem 3.11) proved in their paper “A few remarks on divergent sequences: rate of divergence” [J. Math. Anal. Appl. 360, No. 2, 588–598 (2009; Zbl 1196.40001)]. A new result of the Galambos-Bojanić-Seneta type is proved.
Reviewer: Gerald A. Heuer (Moorhead)
Citations:
Zbl 1196.40001References:
[1] | Bingham, N. H.; Goldie, C. M.; Teugels, J. L., Regular Variation (1987), Cambridge University Press: Cambridge University Press Cambridge · Zbl 0617.26001 |
[2] | Bojanić, R.; Seneta, E., A unified theory of regularly varying sequences, Math. Z., 134, 91-106 (1973) · Zbl 0256.40002 |
[3] | Buldygin, V. V.; Klesov, O. I.; Steinebach, J. G., On some properties of asymptotically quasi-inverse functions, Theory Probab. Math. Statist., 77, 15-30 (2008) · Zbl 1068.26002 |
[4] | Djurčić, D., \(O\)-regularly varying functions and strong asymptotic equivalence, J. Math. Anal. Appl., 220, 451-461 (1998) · Zbl 0920.26004 |
[5] | Djurčić, D.; Božin, V., A proof of a S. Aljančić hypothesis on \(O\)-regularly varying sequences, Publ. Inst. Math. (Beograd), 62, 76, 46-52 (1997) · Zbl 0946.26002 |
[6] | Djurčić, D.; Kočinac, Lj. D.R.; Žižović, M. R., Some properties of rapidly varying sequences, J. Math. Anal. Appl., 327, 1297-1306 (2007) · Zbl 1116.26002 |
[7] | Djurčić, D.; Kočinac, Lj. D.R.; Žižović, M. R., On selection principles and games in divergent processes, (Kočinac, Lj. D.R., Selection Principles and Covering Properties in Topology. Selection Principles and Covering Properties in Topology, Quad. Mat., vol. 18 (2006), Dipartimento di Matematica, Seconda Universita di Napoli: Dipartimento di Matematica, Seconda Universita di Napoli Caserta), 133-155 · Zbl 1168.54002 |
[8] | Djurčić, D.; Kočinac, Lj. D.R.; Žižović, M. R., Rapidly varying sequences and rapid convergence, Topology Appl., 155, 2143-2149 (2008) · Zbl 1154.54002 |
[9] | Djurčić, D.; Kočinac, Lj. D.R.; Žižović, M. R., Classes of sequences of real numbers, games and selection properties, Topology Appl., 156, 46-55 (2008) · Zbl 1168.54002 |
[10] | Djurčić, D.; Kočinac, Lj. D.R.; Žižović, M. R., A few remarks on divergent sequences: rates of divergence, J. Math. Anal. Appl., 360, 588-598 (2009) · Zbl 1196.40001 |
[12] | Djurčić, D.; Torgašev, A., Strong asymptotic equivalence and inversion of functions in the class \(K_c\), J. Math. Anal. Appl., 255, 383-390 (2001) · Zbl 0991.26002 |
[13] | Djurčić, D.; Torgašev, A., Representation theorems for the sequences of the classes \(CR_c\) and \(ER_c\), Siberian Math. J., 45, 834-838 (2004) · Zbl 1054.26001 |
[14] | Djurčić, D.; Torgašev, A., On the Seneta sequences, Acta Math. Sin. (Engl. Ser.), 22, 689-692 (2006) · Zbl 1170.26300 |
[15] | Djurčić, D.; Torgašev, A., Some asymptotic relations for the generalized inverse, J. Math. Anal. Appl., 335, 1397-1402 (2007) · Zbl 1125.26002 |
[16] | Djurčić, D.; Torgašev, A., A theorem of Galambos-Bojanić-Seneta type, Abstr. Appl. Anal., 2009 (2009), Article ID 360794, 6 pp · Zbl 1168.26300 |
[17] | Galambos, J.; Seneta, E., Regularly varying sequences, Proc. Amer. Math. Soc., 41, 110-116 (1973) · Zbl 0247.26002 |
[18] | Karamata, J., Theory and Practice of the Stieltjes Integral, vol. CLIV (1949), Serbian Academy of Sciences and Arts, Institute of Mathematics: Serbian Academy of Sciences and Arts, Institute of Mathematics Belgrade, (in Serbian) |
[20] | Kočinac, Lj. D.R., Selection principles related to \(\alpha_i\)-properties, Taiwanese J. Math., 12, 561-571 (2008) · Zbl 1153.54009 |
[21] | Tasković, M., Fundamental facts on translational \(O\)-regularly varying functions, Math. Morav., 7, 107-152 (2003) · Zbl 1274.26005 |
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