On rough I-convergence of complex uncertain sequences
DOI:
https://doi.org/10.5269/bspm.68335Abstract
In this paper, we introduce the different notion of rough I-convergence of complex uncertain sequence using the concept of I-convergence and rough convergence of complex uncertain sequence namely rough I-convergent almost surely, rough I-convergence in measure, rough I-convergence in distribution, rough I-convergence in mean. Finally, we studied some of their basic properties and examined the relationship among them.
References
[1] A. Esi, S. Debnath, S. Saha, Asymptotically double λ2-statistically equivalent sequences of interval numbers. Mathematica 62(1), 39-46, (2020).
[2] A. Esi, N.Subramanian, A. Esi, The multi rough ideal convergence of difference strongly of χ2 in p-metric spaces defined by Orlicz function. Turkish Journal of Analysis and Number Theory 5(3), 93-100, (2017).
[3] B. Liu, Uncertainty theory, 2nd edition. Springer-Verlag, (2007).
[4] B. Liu, Some research problems in uncertainty theory. J. Uncertain Syst. 3(1), 3-10, (2009).
[5] B. C. Tripathy, P. K. Nath, Statistical convergence of complex uncertain sequences. New Math. Nat. Comput. 13(3), 359-374, (2017).
[6] B. C. Tripathy, B. Hazarika, I -monotonic and I -convergent sequences. Kyungpook Math. J. 51(2), 233-239, (2011).
[7] C. You, L. Yan, The p−distance of uncertain variables. J. Intell. Fuzzy Syst. 32(1), 999-1006, (2017).
[8] C. You, L. Yan, Relationships among convergence concepts of uncertain sequences. Comput. Model. New Technol. 20(3), 12-16, (2016).
[9] E. Dündar, C. Çakan, Rough I -convergence. Gulf J. Math. 2(1), 45-51, (2019).
[10] E. Savas, S. Debnath, D. Rakshit, On I -statistically rough convergence. Publ. Inst. Math. 105(119), 145-150, (2019).
[11] H. Fast, Sur la convergence statistique. Colloq. Math., 2(3-4), 241-244 (1951).
[12] H. Steinhaus, Sur la convergence ordinaire et la convergence asymptotique. Colloq. Math. 2(1), 73-74, (1951).
[13] H. X. Phu , Rough convergence in normed linear spaces. Numer. Funct. Anal. Optim. 22(1-2), 199-222, (2001).
[14] H. X. Phu , Rough convergence in infinite-dimensional normed spaces. Numer. Funct. Anal. Optim. 24, 285-301, (2003).
[15] J. A. Fridy, On statistically convergence. Analysis 5, 301-313, (1985).
[16] M. Mursaleen, S. Debnath, D. Rakshit, I -statistical limit superior and I -statistical limit inferior. Filomat 31(7), 2103-2108, (2017).
[17] N.Subramanian, A. Esi, Rough variables of convergence. Scientific Studies and Research Series Mathematics and Informatics 27(2), 65-72, (2017).
[18] N.Subramanian, A. Esi, Wijsman rough lacunary statistical convergence on I -Cesaro triple sequences. Int. Jour. of Analysis and Applications 16(5), 643-653, (2018).
[19] O. Kisi, Sλ (I)-convergence of complex uncertain sequences. Mat. Stud. 51(2), 183-194, (2019).
[20] P. K. Nath, B. C. Tripathy, Convergent complex uncertain sequences defined by Orlicz function. Ann. Univ. Craiova-Math. Comput. Sci. Ser. 46(1), 139-149, (2019).
[21] P. Kostyrko, M. Macaj, M. Sleziak, and T. Salat, I -convergence. Real Anal. Exchange 26, 669–686, (2000/2001).
[22] S. Debnath, B. Das, On rough statistical convergence of complex uncertain sequences. New Math. Nat. Comput. (2021), doi:10.1142/S1793005722500454.
[23] S. Debnath, B. Das, Statistical convergence of order α for complex uncertain sequences. J.Uncertain Syst. 14(2) (2021), doi:10.1142/S1752890921500124.
[24] S. Debnath, D. Rakshit, Rough convergence in metric space. J. Interdiscip. Multidiscip. Res. 449-554, (2017).
[25] S. Debnath, B. Das, On rough convergence of complex uncertain sequences. J.Uncertain Syst. 14(4) (2021), doi:10.1142/S1752890921500215.
[26] S. Roy, B. C. Tripathy, S. Saha, Some results on p−distance and sequence of complex uncertain variables. Commun. Korean. Math. Soc. 35(3), 907-916, (2020).
[27] S. Saha, B. C. Tripathy, S. Roy, On almost convergence of complex uncertain sequences. New Math. Nat. Comput. 16(03), 573-580, (2020).
[28] T. Ye, Y. Zhu, A metric on uncertain variables. Int. J. Uncertain. Quan. 8, 251-266, (2018).
[29] X. Chen, Y. Ning, X. Wang, Convergence of complex uncertain sequences, J. Intell. Fuzzy Syst., 30(6), 3357-3366, (2016).
[30] Z. Peng, Complex uncertain variable, Doctoral Dissertation, Tsinghua University, (2012).
[2] A. Esi, N.Subramanian, A. Esi, The multi rough ideal convergence of difference strongly of χ2 in p-metric spaces defined by Orlicz function. Turkish Journal of Analysis and Number Theory 5(3), 93-100, (2017).
[3] B. Liu, Uncertainty theory, 2nd edition. Springer-Verlag, (2007).
[4] B. Liu, Some research problems in uncertainty theory. J. Uncertain Syst. 3(1), 3-10, (2009).
[5] B. C. Tripathy, P. K. Nath, Statistical convergence of complex uncertain sequences. New Math. Nat. Comput. 13(3), 359-374, (2017).
[6] B. C. Tripathy, B. Hazarika, I -monotonic and I -convergent sequences. Kyungpook Math. J. 51(2), 233-239, (2011).
[7] C. You, L. Yan, The p−distance of uncertain variables. J. Intell. Fuzzy Syst. 32(1), 999-1006, (2017).
[8] C. You, L. Yan, Relationships among convergence concepts of uncertain sequences. Comput. Model. New Technol. 20(3), 12-16, (2016).
[9] E. Dündar, C. Çakan, Rough I -convergence. Gulf J. Math. 2(1), 45-51, (2019).
[10] E. Savas, S. Debnath, D. Rakshit, On I -statistically rough convergence. Publ. Inst. Math. 105(119), 145-150, (2019).
[11] H. Fast, Sur la convergence statistique. Colloq. Math., 2(3-4), 241-244 (1951).
[12] H. Steinhaus, Sur la convergence ordinaire et la convergence asymptotique. Colloq. Math. 2(1), 73-74, (1951).
[13] H. X. Phu , Rough convergence in normed linear spaces. Numer. Funct. Anal. Optim. 22(1-2), 199-222, (2001).
[14] H. X. Phu , Rough convergence in infinite-dimensional normed spaces. Numer. Funct. Anal. Optim. 24, 285-301, (2003).
[15] J. A. Fridy, On statistically convergence. Analysis 5, 301-313, (1985).
[16] M. Mursaleen, S. Debnath, D. Rakshit, I -statistical limit superior and I -statistical limit inferior. Filomat 31(7), 2103-2108, (2017).
[17] N.Subramanian, A. Esi, Rough variables of convergence. Scientific Studies and Research Series Mathematics and Informatics 27(2), 65-72, (2017).
[18] N.Subramanian, A. Esi, Wijsman rough lacunary statistical convergence on I -Cesaro triple sequences. Int. Jour. of Analysis and Applications 16(5), 643-653, (2018).
[19] O. Kisi, Sλ (I)-convergence of complex uncertain sequences. Mat. Stud. 51(2), 183-194, (2019).
[20] P. K. Nath, B. C. Tripathy, Convergent complex uncertain sequences defined by Orlicz function. Ann. Univ. Craiova-Math. Comput. Sci. Ser. 46(1), 139-149, (2019).
[21] P. Kostyrko, M. Macaj, M. Sleziak, and T. Salat, I -convergence. Real Anal. Exchange 26, 669–686, (2000/2001).
[22] S. Debnath, B. Das, On rough statistical convergence of complex uncertain sequences. New Math. Nat. Comput. (2021), doi:10.1142/S1793005722500454.
[23] S. Debnath, B. Das, Statistical convergence of order α for complex uncertain sequences. J.Uncertain Syst. 14(2) (2021), doi:10.1142/S1752890921500124.
[24] S. Debnath, D. Rakshit, Rough convergence in metric space. J. Interdiscip. Multidiscip. Res. 449-554, (2017).
[25] S. Debnath, B. Das, On rough convergence of complex uncertain sequences. J.Uncertain Syst. 14(4) (2021), doi:10.1142/S1752890921500215.
[26] S. Roy, B. C. Tripathy, S. Saha, Some results on p−distance and sequence of complex uncertain variables. Commun. Korean. Math. Soc. 35(3), 907-916, (2020).
[27] S. Saha, B. C. Tripathy, S. Roy, On almost convergence of complex uncertain sequences. New Math. Nat. Comput. 16(03), 573-580, (2020).
[28] T. Ye, Y. Zhu, A metric on uncertain variables. Int. J. Uncertain. Quan. 8, 251-266, (2018).
[29] X. Chen, Y. Ning, X. Wang, Convergence of complex uncertain sequences, J. Intell. Fuzzy Syst., 30(6), 3357-3366, (2016).
[30] Z. Peng, Complex uncertain variable, Doctoral Dissertation, Tsinghua University, (2012).
Downloads
Published
2025-09-22
Issue
Section
Research Articles
License
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).
How to Cite
Debnath, S., & Halder, A. (2025). On rough I-convergence of complex uncertain sequences. Boletim Da Sociedade Paranaense De Matemática, 43, 1-14. https://doi.org/10.5269/bspm.68335
