On Rough I-Convergence of Complex Uncertain Sequences
On Rough I-Convergence of Complex Uncertain Sequences
Resumo
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.
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Referências
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[2] S. Debnath, B. Das, On rough statistical convergence of complex uncertain sequences, New Math. Nat. Comput., (2021), doi:10.1142/S1793005722500454.
[3] S. Debnath, B. Das, Statistical convergence of order α for complex uncertain sequences, J.Uncertain Syst., 14(2) (2021), doi:10.1142/S1752890921500124.
[4] S. Debnath, D. Rakshit, Rough convergence in metric space, J. Interdiscip. Multidiscip. Res., (2017), 449-554.
[5] S. Debnath, B. Das, On rough convergence of complex uncertain sequences, J.Uncertain Syst., 14(4) (2021), doi:10.1142/S1752890921500215.
[6] E. Dndar, C. akan, Rough I-convergence, Gulf J. Math, 2(1) (2019), 45-51.
[7] A. Esi, S. Debnath, S. Saha Asymptotically double λ2-statistically equivalent sequences of interval numbers, Mathematica, 62(1) (2020), 39-46.
[8] H. Fast, Sur la convergence statistique, Colloq. Math., 2(3-4) (1951), 241-244.
[9] J. A. Fridy, On statistically convergence, Analysis, 5 (1985), 301-313.
[10] O¨. Ki¸si, Sλ(I)-convergence of complex uncertain sequences, Mat. Stud., 51(2) (2019), 183- 194.
[11] P. Kostyrko, M. Maˇ caj, M. Sleziak, and T. Sˇal´ at, I-convergence, Real Anal. Exchange, 26 (2000/2001), 669686.
[12] B. Liu, Uncertainty theory, 2nd edition, Springer-Verlag, (2007).
[13] B. Liu, Some research problems in uncertainty theory, J. Uncertain Syst., 3(1) (2009), 3-10.
[14] M. Mursaleen, S. Debnath, D. Rakshit I-statistical limit superior and I-statistical limit inferior, Filomat, 31(7) (2017), 2103-2108.
[15] P. K. Nath, B. C. Tripathy, Convergent complex uncertain sequences defined by Orlicz function, Ann. Univ. Craiova-Math. Comput. Sci. Ser., 46(1) (2019), 139-149.
[16] Z. Peng, Complex uncertain variable, Doctoral Dissertation, Tsinghua University, 2012.
[17] H. X. Phu , Rough convergence in normed linear spaces, Numer. Funct. Anal. Optim., 22(1- 2) (2001), 199-222.
[18] H. X. Phu , Rough convergence in infinite-dimensional normed spaces, Numer. Funct. Anal. Optim., 24 (2003), 285-301.
[19] S. Roy, B. C. Tripathy, S. Saha, Some results on p−distance and sequence of complex uncertain variables, Commun. Korean. Math. Soc., 35(3) (2020), 907-916.
[20] S. Saha, B. C. Tripathy, S. Roy, On almost convergence of complex uncertain sequences, New Math. Nat. Comput., 16(03) (2020), 573-580.
[21] E. Savas, S. Debnath, D. Rakshit, On I-statistically rough convergence, Publ. Inst. Math., 105(119) (2019), 145-150.
[22] H. Steinhaus, Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math., 2(1) (1951), 73 - 74.
[23] B. C. Tripathy, P. K. Nath, Statistical convergence of complex uncertain sequences, New Math. Nat. Comput., 13(3) (2017), 359-374.
[24] B. C. Tripathy, B. Hazarika, I-monotonic and I-convergent sequences, Kyungpook Math. J., 51(2) (2011), 233-239.
[25] T. Ye, Y. Zhu, A metric on uncertain variables, Int. J. Uncertain. Quan., 8(2018), 251-266.
[26] C. You, L. Yan, The p−distance of uncertain variables, J. Intell. Fuzzy Syst., 32(1) (2017), 999-1006.
[27] C. You, L. Yan, Relationships among convergence concepts of uncertain sequences, Comput. Model. New Technol., 20(3) (2016), 12-16.
[2] S. Debnath, B. Das, On rough statistical convergence of complex uncertain sequences, New Math. Nat. Comput., (2021), doi:10.1142/S1793005722500454.
[3] S. Debnath, B. Das, Statistical convergence of order α for complex uncertain sequences, J.Uncertain Syst., 14(2) (2021), doi:10.1142/S1752890921500124.
[4] S. Debnath, D. Rakshit, Rough convergence in metric space, J. Interdiscip. Multidiscip. Res., (2017), 449-554.
[5] S. Debnath, B. Das, On rough convergence of complex uncertain sequences, J.Uncertain Syst., 14(4) (2021), doi:10.1142/S1752890921500215.
[6] E. Dndar, C. akan, Rough I-convergence, Gulf J. Math, 2(1) (2019), 45-51.
[7] A. Esi, S. Debnath, S. Saha Asymptotically double λ2-statistically equivalent sequences of interval numbers, Mathematica, 62(1) (2020), 39-46.
[8] H. Fast, Sur la convergence statistique, Colloq. Math., 2(3-4) (1951), 241-244.
[9] J. A. Fridy, On statistically convergence, Analysis, 5 (1985), 301-313.
[10] O¨. Ki¸si, Sλ(I)-convergence of complex uncertain sequences, Mat. Stud., 51(2) (2019), 183- 194.
[11] P. Kostyrko, M. Maˇ caj, M. Sleziak, and T. Sˇal´ at, I-convergence, Real Anal. Exchange, 26 (2000/2001), 669686.
[12] B. Liu, Uncertainty theory, 2nd edition, Springer-Verlag, (2007).
[13] B. Liu, Some research problems in uncertainty theory, J. Uncertain Syst., 3(1) (2009), 3-10.
[14] M. Mursaleen, S. Debnath, D. Rakshit I-statistical limit superior and I-statistical limit inferior, Filomat, 31(7) (2017), 2103-2108.
[15] P. K. Nath, B. C. Tripathy, Convergent complex uncertain sequences defined by Orlicz function, Ann. Univ. Craiova-Math. Comput. Sci. Ser., 46(1) (2019), 139-149.
[16] Z. Peng, Complex uncertain variable, Doctoral Dissertation, Tsinghua University, 2012.
[17] H. X. Phu , Rough convergence in normed linear spaces, Numer. Funct. Anal. Optim., 22(1- 2) (2001), 199-222.
[18] H. X. Phu , Rough convergence in infinite-dimensional normed spaces, Numer. Funct. Anal. Optim., 24 (2003), 285-301.
[19] S. Roy, B. C. Tripathy, S. Saha, Some results on p−distance and sequence of complex uncertain variables, Commun. Korean. Math. Soc., 35(3) (2020), 907-916.
[20] S. Saha, B. C. Tripathy, S. Roy, On almost convergence of complex uncertain sequences, New Math. Nat. Comput., 16(03) (2020), 573-580.
[21] E. Savas, S. Debnath, D. Rakshit, On I-statistically rough convergence, Publ. Inst. Math., 105(119) (2019), 145-150.
[22] H. Steinhaus, Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math., 2(1) (1951), 73 - 74.
[23] B. C. Tripathy, P. K. Nath, Statistical convergence of complex uncertain sequences, New Math. Nat. Comput., 13(3) (2017), 359-374.
[24] B. C. Tripathy, B. Hazarika, I-monotonic and I-convergent sequences, Kyungpook Math. J., 51(2) (2011), 233-239.
[25] T. Ye, Y. Zhu, A metric on uncertain variables, Int. J. Uncertain. Quan., 8(2018), 251-266.
[26] C. You, L. Yan, The p−distance of uncertain variables, J. Intell. Fuzzy Syst., 32(1) (2017), 999-1006.
[27] C. You, L. Yan, Relationships among convergence concepts of uncertain sequences, Comput. Model. New Technol., 20(3) (2016), 12-16.
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2025-09-22
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