On $\mathcal{i}_{2}$ and $\mathcal{i}_{2}^{\ast}$-convergence in almost surely of complex uncertain double sequences
Problemy analiza, Tome 12 (2023) no. 2, pp. 51-67.

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In this study, we investigate the notions of $\mathcal{I}_{2}$-convergence almost surely (a.s.) and $\mathcal{I}_{2}^{\ast }$-convergence a.s. of complex uncertain double sequences in an uncertainty space, and obtain some of their features and identify the relationships between them. In addition, we put forward the concepts of $\mathcal{I}_{2}$ and $\mathcal{I} _{2}^{\ast }$-Cauchy sequence a.s. of complex uncertain double sequences and investigate their relationships.
Keywords: uncertainty theory, complex uncertain variable, $\mathcal{I}_{2}$-convergence, $\mathcal{I}_{2}^{\ast}$-convergence.
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Ö. Kişi; M. Gürdal. On $\mathcal{i}_{2}$ and $\mathcal{i}_{2}^{\ast}$-convergence in almost surely of complex uncertain double sequences. Problemy analiza, Tome 12 (2023) no. 2, pp. 51-67. http://geodesic.mathdoc.fr/item/PA_2023_12_2_a3/

[1] Chen X., Ning Y., Wang X., “Convergence of complex uncertain sequences”, J. Intell. Fuzzy Syst., 30:6 (2016), 3357–3366 | DOI | Zbl

[2] Das P., Kostyrko P., Wilczyński W., Malik P., “$\mathcal{I} $ and $\mathcal{I}^{\ast }$-convergence of double sequences”, Math. Slovaca, 58:5 (2008), 605–620 | DOI | MR | Zbl

[3] Das B., Tripathy B. C., Debnath P., Bhattacharya B., “Almost convergence of complex uncertain double sequences”, Filomat, 35:1 (2021), 61–78 | DOI | MR | Zbl

[4] Das B., Tripathy B. C., Debnath P., Bhattacharya B., “Characterization of statistical convergence of complex uncertain double sequence”, Anal. Math. Phys., 10:71 (2020), 1–20 | DOI | MR

[5] Datta D., Tripathy B. C., “Convergence of complex uncertain double sequences”, New Math. Nat. Comput., 16:3 (2020), 447–459 | DOI | MR

[6] Dndar E., Altay B., “$\mathcal{I}_{2}$-convergence and $\mathcal{I}_{2}$-Cauchy double sequences”, Acta Math. Sci., 34:2 (2014), 343–353 | DOI | MR

[7] Fast F., “Sur la convergence statistique”, Colloq. Math., 2 (1951), 241–244 | DOI | MR | Zbl

[8] Fridy J. A., “On statistical convergence”, Analysis, 5:4 (1985), 301–313 | DOI | MR | Zbl

[9] Gürdal M., Huban M. B., “On $\mathcal{I}$-convergence of double sequences in the topology induced by random 2-norms”, Mat. Vesnik, 66:1 (2014), 73–83 | MR | Zbl

[10] Gürdal M., Şahiner A., “Extremal $\mathcal{I}$-limit points of double sequences”, Appl. Math. E-Notes, 88 (2008), 131–137 | MR

[11] Kişi Ö., “$S_{\lambda} (\mathcal{I})$-convergence of complex uncertain sequences”, Mat. Stud., 51:2 (2019), 183–194 | MR | Zbl

[12] Kostyrko P., S̆alát T., Wilczyński W., “$\mathcal{I}$-convergence”, Real Anal. Exchange, 26:2 (2000), 669–686 | DOI | MR

[13] Liu B., Uncertainty Theory, 2nd edn., Springer, Berlin, 2007 | MR | Zbl

[14] Liu B., “Uncertain risk analysis and uncertain reliability analysis”, J. Uncertain Syst., 4:3 (2010), 163–170

[15] Mohiuddine S. A., Alamri B. A. S., “Generalization of equi-statistical convergence via weighted lacunary sequence with associated Korovkin and Voronovskaya type approximation theorems”, Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Math., 113:3 (2019), 1955–1973 | DOI | MR | Zbl

[16] Moricz F., “Statistical convergence of multiple sequences”, Arch. Math., 81 (2003), 82–89 | DOI | MR | Zbl

[17] Mursaleen M., Edely O. H. H., “Statistical convergence of double sequences”, J. Math. Anal. Appl., 288:1 (2003), 223–231 | DOI | MR | Zbl

[18] Nabiev A., Pehlivan S., Gürdal M., “On $\mathcal{I}$-Cauchy sequences”, Taiwanese J. Math., 12 (2007), 569–576 | MR

[19] Peng Z., Iwamura K., “A sufficient and necessary condition of uncertainty distribution”, J. Interdiscip. Math., 13:3 (2010), 277–285 | DOI | MR | Zbl

[20] Saha S., Tripathy B. C., Roy S., “On almost convergence of complex uncertain sequences”, New Math. Nat. Comput., 16:3 (2020), 573–580 | DOI | MR

[21] Savaş E., Gürdal M., “Generalized statistically convergent sequences of functions in fuzzy $2$-normed spaces”, J. Intell. Fuzzy Systems, 27:4 (2014), 2067–2075 | DOI | MR | Zbl

[22] Savaş E., Gürdal M., “Ideal convergent function sequences in random $2$-normed spaces”, Filomat, 30:3 (2016), 557–567 | DOI | MR | Zbl

[23] Tripathy B. C., “Statistically convergent double sequences”, Tamkang J. Math., 34:3 (2003), 231–237 | DOI | MR | Zbl

[24] Tripathy B. C., Nath P. K., “Statistical convergence of complex uncertain sequences”, New Math. Nat. Comput., 13 (2017), 359–374 | DOI | MR