On rough I-convergence of complex uncertain sequences
Abstract
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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A. Esi, S. Debnath, S. Saha, Asymptotically double λ2-statistically equivalent sequences of interval numbers. Mathematica 62(1), 39-46, (2020).
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).
B. Liu, Uncertainty theory, 2nd edition. Springer-Verlag, (2007).
B. Liu, Some research problems in uncertainty theory. J. Uncertain Syst. 3(1), 3-10, (2009).
B. C. Tripathy, P. K. Nath, Statistical convergence of complex uncertain sequences. New Math. Nat. Comput. 13(3), 359-374, (2017).
B. C. Tripathy, B. Hazarika, I -monotonic and I -convergent sequences. Kyungpook Math. J. 51(2), 233-239, (2011).
C. You, L. Yan, The p−distance of uncertain variables. J. Intell. Fuzzy Syst. 32(1), 999-1006, (2017).
C. You, L. Yan, Relationships among convergence concepts of uncertain sequences. Comput. Model. New Technol. 20(3), 12-16, (2016).
E. Dündar, C. Çakan, Rough I -convergence. Gulf J. Math. 2(1), 45-51, (2019).
E. Savas, S. Debnath, D. Rakshit, On I -statistically rough convergence. Publ. Inst. Math. 105(119), 145-150, (2019).
H. Fast, Sur la convergence statistique. Colloq. Math., 2(3-4), 241-244 (1951).
H. Steinhaus, Sur la convergence ordinaire et la convergence asymptotique. Colloq. Math. 2(1), 73-74, (1951).
H. X. Phu , Rough convergence in normed linear spaces. Numer. Funct. Anal. Optim. 22(1-2), 199-222, (2001).
H. X. Phu , Rough convergence in infinite-dimensional normed spaces. Numer. Funct. Anal. Optim. 24, 285-301, (2003).
J. A. Fridy, On statistically convergence. Analysis 5, 301-313, (1985).
M. Mursaleen, S. Debnath, D. Rakshit, I -statistical limit superior and I -statistical limit inferior. Filomat 31(7), 2103-2108, (2017).
N.Subramanian, A. Esi, Rough variables of convergence. Scientific Studies and Research Series Mathematics and Informatics 27(2), 65-72, (2017).
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).
O. Kisi, Sλ (I)-convergence of complex uncertain sequences. Mat. Stud. 51(2), 183-194, (2019).
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).
P. Kostyrko, M. Macaj, M. Sleziak, and T. Salat, I -convergence. Real Anal. Exchange 26, 669–686, (2000/2001).
S. Debnath, B. Das, On rough statistical convergence of complex uncertain sequences. New Math. Nat. Comput. (2021), doi:10.1142/S1793005722500454.
S. Debnath, B. Das, Statistical convergence of order α for complex uncertain sequences. J.Uncertain Syst. 14(2) (2021), doi:10.1142/S1752890921500124.
S. Debnath, D. Rakshit, Rough convergence in metric space. J. Interdiscip. Multidiscip. Res. 449-554, (2017).
S. Debnath, B. Das, On rough convergence of complex uncertain sequences. J.Uncertain Syst. 14(4) (2021), doi:10.1142/S1752890921500215.
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).
S. Saha, B. C. Tripathy, S. Roy, On almost convergence of complex uncertain sequences. New Math. Nat. Comput. 16(03), 573-580, (2020).
T. Ye, Y. Zhu, A metric on uncertain variables. Int. J. Uncertain. Quan. 8, 251-266, (2018).
X. Chen, Y. Ning, X. Wang, Convergence of complex uncertain sequences, J. Intell. Fuzzy Syst., 30(6), 3357-3366, (2016).
Z. Peng, Complex uncertain variable, Doctoral Dissertation, Tsinghua University, (2012).
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