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More on Translationally Slowly Varying Sequences

Year 2019, Volume: 1 Issue: 1, 24 - 29, 09.04.2019

Dragan Djurcic Ljubiša D. R. Kočinac

Abstract

We define and study an equivalence relation in the class ${\sf Tr(SV_s)}$ of translationally slowly varying positive real sequences and its relations with selection principles and game theory. We also prove a game-theoretic result for translationally rapidly varying sequences.

Keywords

Rapid equivalence Class $R_{s;\infty}$ Selection principles

References

  • [1] N.H. Bingham, C.M. Goldie, J.L. Teugels, Regular Variation, CambridgeUniv. Press, Cambridge, 1987.
  • [2] D. Djurcic, Lj.D.R. Kocinac, M.R. Zizovic, Some properties of rapidly varying sequences, J. Math. Anal. Appl. 327:2 (2007) 1297-1306.
  • [3] D. Djuric, Lj.D.R. Kocinac, M.R. Zizovic, Classes of sequences of real numbers, games and selection properties, Topology Appl. 156:1 (2008) 46-55.
  • [4] D. Djurcic, Lj.D.R. Kocinac, M.R. Zizovic, A few remarks on divergent sequences: Rates of divergence, J. Math. Anal. Appl. 360:2 (2009) 588-598.
  • [5] D. Djurcic, Lj.D.R. Kocinac, M.R. Zizovic, A few remarks on divergent sequences: rates of divergence II, J. Math. Anal. Appl. 367:2 (2010) 705-709.
  • [6] D. Djurcic, A. Torgasev, S. Jesic, The strong asymptotic equivalence and the generalized inverse, Siber. Math. J. 49:4 (2008) 786-795.
  • [7] L. de Haan, On Regular Variation and its Applications to the Weak Convergence of Sample Extremes, Math. Centre Tracts, Vol. 32, CWI, Amsterdam, 1970.
  • [8] J. Karamata, Sur un mode de croissance reguliere des functions, Mathematica(Cluj) 4 (1930) 38-53.
  • [9] Lj.D.R. Kocinac, Selected results on selection principle, In: Proc. Third.Sem. Geom. Topology, Tabriz, Iran (2004) 71-104.
  • [10] Lj.D.R. Kocinac, On the ®i-selection principles and games, Cont. Math.533 (2011) 107-124.
  • [11] Lj.D.R. Kocinac, D. Djurcic, J.V. Manojlovic, Regular and Rapid Variations and Some Applications, In: M. Ruzhansky, H. Dutta, R.P. Agarwal(eds.), Mathematical Analysis and Applications: Selected Topics, Chapter12, John Wiley & Sons, Inc., (2018) 414-474.
  • [12] V. Timotic, D. Djurcic, R.M. Nikolic, On slowly varying sequences, Filomat29:1 (2015) 7-12

Year 2019, Volume: 1 Issue: 1, 24 - 29, 09.04.2019

Dragan Djurcic Ljubiša D. R. Kočinac

Abstract

References

  • [1] N.H. Bingham, C.M. Goldie, J.L. Teugels, Regular Variation, CambridgeUniv. Press, Cambridge, 1987.
  • [2] D. Djurcic, Lj.D.R. Kocinac, M.R. Zizovic, Some properties of rapidly varying sequences, J. Math. Anal. Appl. 327:2 (2007) 1297-1306.
  • [3] D. Djuric, Lj.D.R. Kocinac, M.R. Zizovic, Classes of sequences of real numbers, games and selection properties, Topology Appl. 156:1 (2008) 46-55.
  • [4] D. Djurcic, Lj.D.R. Kocinac, M.R. Zizovic, A few remarks on divergent sequences: Rates of divergence, J. Math. Anal. Appl. 360:2 (2009) 588-598.
  • [5] D. Djurcic, Lj.D.R. Kocinac, M.R. Zizovic, A few remarks on divergent sequences: rates of divergence II, J. Math. Anal. Appl. 367:2 (2010) 705-709.
  • [6] D. Djurcic, A. Torgasev, S. Jesic, The strong asymptotic equivalence and the generalized inverse, Siber. Math. J. 49:4 (2008) 786-795.
  • [7] L. de Haan, On Regular Variation and its Applications to the Weak Convergence of Sample Extremes, Math. Centre Tracts, Vol. 32, CWI, Amsterdam, 1970.
  • [8] J. Karamata, Sur un mode de croissance reguliere des functions, Mathematica(Cluj) 4 (1930) 38-53.
  • [9] Lj.D.R. Kocinac, Selected results on selection principle, In: Proc. Third.Sem. Geom. Topology, Tabriz, Iran (2004) 71-104.
  • [10] Lj.D.R. Kocinac, On the ®i-selection principles and games, Cont. Math.533 (2011) 107-124.
  • [11] Lj.D.R. Kocinac, D. Djurcic, J.V. Manojlovic, Regular and Rapid Variations and Some Applications, In: M. Ruzhansky, H. Dutta, R.P. Agarwal(eds.), Mathematical Analysis and Applications: Selected Topics, Chapter12, John Wiley & Sons, Inc., (2018) 414-474.
  • [12] V. Timotic, D. Djurcic, R.M. Nikolic, On slowly varying sequences, Filomat29:1 (2015) 7-12
There are 12 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Dragan Djurcic This is me

Ljubiša D. R. Kočinac

Publication Date April 9, 2019
Acceptance Date March 20, 2019
Published in Issue Year 2019 Volume: 1 Issue: 1

Cite

APA Djurcic, D., & Kočinac, L. D. R. (2019). More on Translationally Slowly Varying Sequences. Maltepe Journal of Mathematics, 1(1), 24-29.
AMA Djurcic D, Kočinac LDR. More on Translationally Slowly Varying Sequences. Maltepe Journal of Mathematics. April 2019;1(1):24-29.
Chicago Djurcic, Dragan, and Ljubiša D. R. Kočinac. “More on Translationally Slowly Varying Sequences”. Maltepe Journal of Mathematics 1, no. 1 (April 2019): 24-29.
EndNote Djurcic D, Kočinac LDR (April 1, 2019) More on Translationally Slowly Varying Sequences. Maltepe Journal of Mathematics 1 1 24–29.
IEEE D. Djurcic and L. D. R. Kočinac, “More on Translationally Slowly Varying Sequences”, Maltepe Journal of Mathematics, vol. 1, no. 1, pp. 24–29, 2019.
ISNAD Djurcic, Dragan - Kočinac, Ljubiša D. R. “More on Translationally Slowly Varying Sequences”. Maltepe Journal of Mathematics 1/1 (April 2019), 24-29.
JAMA Djurcic D, Kočinac LDR. More on Translationally Slowly Varying Sequences. Maltepe Journal of Mathematics. 2019;1:24–29.
MLA Djurcic, Dragan and Ljubiša D. R. Kočinac. “More on Translationally Slowly Varying Sequences”. Maltepe Journal of Mathematics, vol. 1, no. 1, 2019, pp. 24-29.
Vancouver Djurcic D, Kočinac LDR. More on Translationally Slowly Varying Sequences. Maltepe Journal of Mathematics. 2019;1(1):24-9.
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