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Asymptotically J_σ-Equivalence of Sequences of Sets

Year 2019, Volume: 23 Issue: 5, 718 - 723, 01.10.2019
https://doi.org/10.16984/saufenbilder.509863

Abstract

In this
study, we introduce the concepts of Wijsman asymptotically J-
invariant equivalence (WLJσ) , Wijsman asymptotically strongly p-invariant equivalence ([WLVσ)]p) and Wijsman asymptotically J*-invariant equivalence (WLJ*σ). Also, we investigate the relationships among the concepts
of Wijsman asymptotically invariant equivalence, Wijsman asymptotically
invariant statistical equivalence, 
WLJσ[WLVσ)]p and WLJ*σ

References

  • [1] Ö. Kişi and F. Nuray, “On S_λ^L (J)-asymptotically statistical equivalence of sequences of sets”, ISRN Mathematical Analysis, vol. 2013, Article ID 602963, 6 pages, 2013. doi:10.1155/2013/602963
  • [2] P. Kostyrko, W. Wilczyński and T. Šalát, “J-convergence”, Real Anal. Exchange, vol. 26, no. 2, pp. 669–686, 2000.
  • [3] M. Marouf, “Asymptotic equivalence and summability”, Int. J. Math. Math. Sci., vol 16, no. 4, pp. 755–762, 1993.
  • [4] M. Mursaleen, “Matrix transformation between some new sequence spaces”, Houston J. Math., vol. 9, no. 4, pp. 505–509, 1983.
  • [5] F. Nuray, H. Gök and U. Ulusu, “J_σ-convergence”, Math. Commun., vol.16, pp. 531–538, 2011.
  • [6] F. Nuray and B. E. Rhoades, “Statistical convergence of sequences of sets”, Fasc. Math., vol. 49, pp. 87–99, 2012.
  • [7] N. Pancaroğlu and F. Nuray, “On invariant statistically convergence and lacunary invariant statistically convergence of sequences of sets”, Progress in Applied Mathematics, vol. 5, no. 2, pp. 23–29, 2013.
  • [8] N. Pancaroğlu, F. Nuray and E. Savaş, “On asymptotically lacunary invariant statistical equivalent set sequences”, AIP Conf. Proc., vol. 1558, no. 1, pp. 780–781, 2013. doi:10.1063/1.4825609
  • [9] E. Savaş, “Strongly σ-convergent sequences”, Bull. Calcutta Math., vol. 81, pp. 295–300, 1989.
  • [10] E. Savaş and F. Nuray, “On σ-statistically convergence and lacunary σ-statistically convergence”, Math. Slovaca, vol. 43, no. 3, pp. 309–315, 1993.
  • [11] U. Ulusu and F. Nuray, “On asymptotically lacunary statistical equivalent set sequences”, Journal of Mathematics, vol. 2013, Article ID 310438, 5 pages, 2013. doi:10.1155/2013/310438
Year 2019, Volume: 23 Issue: 5, 718 - 723, 01.10.2019
https://doi.org/10.16984/saufenbilder.509863

Abstract

References

  • [1] Ö. Kişi and F. Nuray, “On S_λ^L (J)-asymptotically statistical equivalence of sequences of sets”, ISRN Mathematical Analysis, vol. 2013, Article ID 602963, 6 pages, 2013. doi:10.1155/2013/602963
  • [2] P. Kostyrko, W. Wilczyński and T. Šalát, “J-convergence”, Real Anal. Exchange, vol. 26, no. 2, pp. 669–686, 2000.
  • [3] M. Marouf, “Asymptotic equivalence and summability”, Int. J. Math. Math. Sci., vol 16, no. 4, pp. 755–762, 1993.
  • [4] M. Mursaleen, “Matrix transformation between some new sequence spaces”, Houston J. Math., vol. 9, no. 4, pp. 505–509, 1983.
  • [5] F. Nuray, H. Gök and U. Ulusu, “J_σ-convergence”, Math. Commun., vol.16, pp. 531–538, 2011.
  • [6] F. Nuray and B. E. Rhoades, “Statistical convergence of sequences of sets”, Fasc. Math., vol. 49, pp. 87–99, 2012.
  • [7] N. Pancaroğlu and F. Nuray, “On invariant statistically convergence and lacunary invariant statistically convergence of sequences of sets”, Progress in Applied Mathematics, vol. 5, no. 2, pp. 23–29, 2013.
  • [8] N. Pancaroğlu, F. Nuray and E. Savaş, “On asymptotically lacunary invariant statistical equivalent set sequences”, AIP Conf. Proc., vol. 1558, no. 1, pp. 780–781, 2013. doi:10.1063/1.4825609
  • [9] E. Savaş, “Strongly σ-convergent sequences”, Bull. Calcutta Math., vol. 81, pp. 295–300, 1989.
  • [10] E. Savaş and F. Nuray, “On σ-statistically convergence and lacunary σ-statistically convergence”, Math. Slovaca, vol. 43, no. 3, pp. 309–315, 1993.
  • [11] U. Ulusu and F. Nuray, “On asymptotically lacunary statistical equivalent set sequences”, Journal of Mathematics, vol. 2013, Article ID 310438, 5 pages, 2013. doi:10.1155/2013/310438
There are 11 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Uğur Ulusu 0000-0001-7658-6114

Esra Gülle 0000-0001-5575-2937

Publication Date October 1, 2019
Submission Date January 8, 2019
Acceptance Date March 1, 2019
Published in Issue Year 2019 Volume: 23 Issue: 5

Cite

APA Ulusu, U., & Gülle, E. (2019). Asymptotically J_σ-Equivalence of Sequences of Sets. Sakarya University Journal of Science, 23(5), 718-723. https://doi.org/10.16984/saufenbilder.509863
AMA Ulusu U, Gülle E. Asymptotically J_σ-Equivalence of Sequences of Sets. SAUJS. October 2019;23(5):718-723. doi:10.16984/saufenbilder.509863
Chicago Ulusu, Uğur, and Esra Gülle. “Asymptotically J_σ-Equivalence of Sequences of Sets”. Sakarya University Journal of Science 23, no. 5 (October 2019): 718-23. https://doi.org/10.16984/saufenbilder.509863.
EndNote Ulusu U, Gülle E (October 1, 2019) Asymptotically J_σ-Equivalence of Sequences of Sets. Sakarya University Journal of Science 23 5 718–723.
IEEE U. Ulusu and E. Gülle, “Asymptotically J_σ-Equivalence of Sequences of Sets”, SAUJS, vol. 23, no. 5, pp. 718–723, 2019, doi: 10.16984/saufenbilder.509863.
ISNAD Ulusu, Uğur - Gülle, Esra. “Asymptotically J_σ-Equivalence of Sequences of Sets”. Sakarya University Journal of Science 23/5 (October 2019), 718-723. https://doi.org/10.16984/saufenbilder.509863.
JAMA Ulusu U, Gülle E. Asymptotically J_σ-Equivalence of Sequences of Sets. SAUJS. 2019;23:718–723.
MLA Ulusu, Uğur and Esra Gülle. “Asymptotically J_σ-Equivalence of Sequences of Sets”. Sakarya University Journal of Science, vol. 23, no. 5, 2019, pp. 718-23, doi:10.16984/saufenbilder.509863.
Vancouver Ulusu U, Gülle E. Asymptotically J_σ-Equivalence of Sequences of Sets. SAUJS. 2019;23(5):718-23.