I and I*-soft convergence in soft topological spaces
Resumen
In this paper, we introduce the notions of I and I*-soft convergence of sequences of soft points in soft topological spaces and study some basic properties of these notions. Also we introduce the notions of I-soft limit points and I-soft cluster points of a sequence of soft points in a soft topological space and study their interrelationship.
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Citas
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26. D. Molodtsov, Soft set theory-first results, Computers and mathematics with applications, 37 (4-5) (1999) 19 - 31. https://doi.org/10.1016/S0898-1221(99)00056-5
27. T. Salat, On statistically convergent sequences of real numbers, Mathematica Slovaca, 30 (2) (1980) 139 - 150.http://dml.cz/dmlcz/136236
28. E. Savas, P. Das and S. Dutta, A note on strong matrix summability via ideals, Applied Mathematics Letters, 25 (4) (2012) 733 - 738. https://doi.org/10.1016/j.aml.2011.10.012
29. I. J. Schoenberg, The integrability of certain functions and related summability methods, The American mathematical monthly, 66 (5) (1959) 361 - 775. https://doi.org/10.2307/2308747
30. M. Shabir and M. Naz, On soft topological spaces, Computers and Mathematics with Applications, 61 (2011) 1786-1799. http://dx.doi.org/10.1016/j.camwa.2011.02.006.
31. N. Xie, Soft points and the structure of soft topological spaces, Annals of Fuzzy Mathematics and Informatics, 10 (2) (2015) 309 - 322.
32. I. Zorlutuna, M. Akdag, W. K. Min and S. Atmaca, Remarks on soft topological spaces, Annals of Fuzzy Mathematics and Informatics, 3 (2) (2012) 171 - 185.
2. H. Aktas and N. Ca˘gman, Soft sets and soft groups, Information Sciences, 177 (13) (2007) 2726 -2735. https://doi.org/10.1016/j.ins.2006.12.008
3. M. I. Ali, F. Feng and X. Liu, W. K. Min, M. Shabir, On some new operations in soft set theory, Computers and mathematics with applications, 57 (9) (2009) 1547 - 1553. https://doi.org/10.1016/j.camwa.2008.11.009
4. A. Aygunoglu and H. Aygun, Some notes on soft topological spaces, Neural Computing and Applications, 21 (2012) 113 -119. https://doi.org/10.1007/s00521-011-0722-3
5. E. Bayrama and M. Dervisoglua, Weighted statistical soft convergence in soft topologies, Filomat, 39 (2) (2025) 501 -514. https://doi.org/10.2298/FIL2502501B
6. S. Bayramov, C. G. Aras and V. Cafarli, Soft countable topological spaces, Transactions of National Academy of Sciences of Azerbaijan. Series of Physical-Technical and Mathematical Sciences, 39 (1) (2019) 15-23. https://trans.imm.az/volumes/39-1/3901-02.pdf
7. N. Cagman, S. KarataS¸ and S. Enginoglu, Soft topology, Computers and Mathematics with Applications, 62 (351-358) (2011) 351 - 358. https://doi.org/10.1016/j.camwa.2011.05.016
8. J. S. Connor, The statistical and strong p-Cesaro convergence of sequences, Analysis, 8 (1-2) (1988), 47-64.
9. S. Das and S. K. Samanta, Soft metric, Annals of Fuzzy Mathematics and Informatics, 20 (1) (2013) 77 - 94.
10. I. DemIr and O. B. Ozbakir, Soft Hausdorff spaces and their some properties, Annals of Fuzzy Mathematics and Informatics Inform, 8 (5) (2014) 769 - 783.
11. G. Di Maio and L. A. D. Kocinac, Statistical convergence in topology, Topology and its Applications, 156 (1) (2008) 28 - 45. https://doi.org/10.1016/j.topol.2008.01.015
12. H. Fast, Sur la convergence statistique, Colloquium mathematicae, 2 (1951) 241-244.
13. A. Freedman and J. Sember, Densities and summability, Pacific Journal of Mathematics, 95 (2) (1981) 293-305. https://msp.org/pjm/1981/95-2/p05.xhtml
14. J. A. Fridy, On statistical convergence, Analysis, 5 (4) (1985) 301 -314. https://doi.org/10.1524/anly.1985.5.4.301
15. J. A. Fridy, Statistical limit points, Proceedings of the American mathematical society, 118 (4) (1993) 1187 - 1192. https://doi.org/10.1090/S0002-9939-1993-1181163-6
16. M. Gurdal and H. Sari, Extremal A-statistical limit points via ideals, Journal of the Egyptian Mathematical Society, 22 (1) (2014) 55-58. https://doi.org/10.1016/j.joems.2013.06.005
17. S. Hussain and B. Ahmad, Soft separation axioms in soft topological spaces, Hacettepe Journal of Mathematics and Statistics, 44 (3) (2015) 559 - 568. Doi : 10.15672/HJMS.2015449426
18. A. Iguda, Soft Sets and Soft Topological Notions, Journal of New Theory, 30 (2020) 21 - 34. https://izlik.org/JA49CD76NS
19. S. A. Jubair and M. H. Ajam, On the Stability of Soft Fixed Point in Soft Topological Space, International Journal of Mathematics Trends and Technology-IJMTT, 69 (10) (2023) 31 - 38. https://doi.org/10.14445/22315373/IJMTTV69I10P505
20. E. Kolk, The statistical convergence in Banach spaces, Acta et Commentationes Universitatis Tartuensis, 928 (1991) 41-52.
21. P. Kostyrko, W. Wilczynski and T. Salat, I-convergence, Real Analysis Exchange, 26 (2) (2000) 669 - 686.
22. K. Kuratowski, Topologie, I. PWN, Warszawa, (1962).
23. B. K. Lahiri and P. Das, I and I∗-convergence in topological spaces, Mathematica bohemica, 130 (2) (2005) 153- 160. http://dml.cz/dmlcz/134133
24. P. K. Maji, R. Biswas and A. R. Roy, Soft set theory, Computers and mathematics with applications, 45 (4-5) (2003) 555 -562. https://doi.org/10.1016/S0898-1221(03)00016-6
25. P. Malik and S. Das, A study on strong AI-statistical convergence of sequences in probabilistic metric spaces, Annals of the University of Craiova - Mathematics and Computer Science Series, 50 (1) (2023) 99 -115. http://inf.ucv.ro/ ami/index.php/ami/article/view/1633
26. D. Molodtsov, Soft set theory-first results, Computers and mathematics with applications, 37 (4-5) (1999) 19 - 31. https://doi.org/10.1016/S0898-1221(99)00056-5
27. T. Salat, On statistically convergent sequences of real numbers, Mathematica Slovaca, 30 (2) (1980) 139 - 150.http://dml.cz/dmlcz/136236
28. E. Savas, P. Das and S. Dutta, A note on strong matrix summability via ideals, Applied Mathematics Letters, 25 (4) (2012) 733 - 738. https://doi.org/10.1016/j.aml.2011.10.012
29. I. J. Schoenberg, The integrability of certain functions and related summability methods, The American mathematical monthly, 66 (5) (1959) 361 - 775. https://doi.org/10.2307/2308747
30. M. Shabir and M. Naz, On soft topological spaces, Computers and Mathematics with Applications, 61 (2011) 1786-1799. http://dx.doi.org/10.1016/j.camwa.2011.02.006.
31. N. Xie, Soft points and the structure of soft topological spaces, Annals of Fuzzy Mathematics and Informatics, 10 (2) (2015) 309 - 322.
32. I. Zorlutuna, M. Akdag, W. K. Min and S. Atmaca, Remarks on soft topological spaces, Annals of Fuzzy Mathematics and Informatics, 3 (2) (2012) 171 - 185.
Publicado
2026-04-09
Sección
Special Issue: Advances in Mathematical Sciences
Derechos de autor 2026 Boletim da Sociedade Paranaense de Matemática
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