A Generalized of Sλ-I-Convergence of Complex Uncertain Double Sequences
Main Article Content
Keywords
λI2-convergence, uncertainty theory, complex uncertain variable, ideal spaces
Abstract
In this paper, we introduce the λI2 -statistically convergence sequence concepts which are namely λI2 -statistically convergence almost surely (Sλ(I2) a.s.), λI2 -statistically convergence in measure, λI2 -statistically
convergence in mean, λI2 -statistically convergence in distribution and λI2 -statistically convergence uniformly almost surely (Sλ(I2) u.a.s.). Additionally, decomposition theorems and relationships among them are presented, further, when reciprocal of one theorem is not satisfied, an counterexample is shown to support the result.
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References
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[15] B. Liu and X. Chen, “ Uncertain multiobjective programming and uncertain goal programming,” Journal of Uncertainty Analysis and Applications, vol. 3, pp. 1–10, 2015. https://doi.org/10.1186/s40467-015-0036-6
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[19] K. Yao and X. Chen, “A numerical method for solving uncertain differential equations,” Journal of Intelligent & Fuzzy Systems, vol. 25, no. 3, pp. 825–832, 2013. https://doi.org/10.3233/IFS-120688
[20] X. Gao and Y. Gao, “Connectedness index of uncertain graphs,” International Journal of Uncertainty, Fuzziness & Knowledge-Based Systems, vol. 21, no. 1, pp. 127–137, 2013. https://doi.org/10.1142/S0218488513500074
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[22] X. Chen, “American option pricing formula for uncertain financial market,” International Journal of Operations Research, vol. 8, no. 2, pp. 32–37, 2011.
[23] B. Liu, “Toward uncertain finance theory,” Journal of Uncertainty Analysis and Applications, vol. 1, pp. 3–16, 2013.
[24] O. Kisi and H. Unal, “ Lacunary statistical convergence of complex uncertain sequence,” Sigma J. Eng. & Nat. Sci., vol. 10, no. 3, pp. 277–286, 2019. https://doi.org/10.5269/bspm.52688
[25] O. Kisi, “The λ-statistically convergent double sequences in fuzzy normed spaces,” hermal Science, vol. 23, no. 1, pp. 153–163, 2019.
[26] O. Kisi, “I2-λ-statistically convergence of double sequences in fuzzy normed spaces,” Journal of Intelligent and Fuzzy Systems, vol. 36, no. 4, pp. 3637–3648, 2019. https://doi.org/10.18514/MMN.2015.821
[27] Z. Peng, Complex uncertain variable. Doctoral Dissertation-Tsinghua University, 2012.
[28] C. You, “On the convergence of uncertain sequences,” Mathematical and Computer Modelling, vol. 49, no. 3–4, pp. 482–487, 2009.
https://doi.org/10.1016/j.mcm.2008.07.007
[29] H. Guo and C. Xu, “A necessary and sufficient condition of convergence in mean square for uncertain sequence,” Information: An International Interdisciplinary Journal, vol. 16, no. 2A, pp. 1091–1096, 2013.
[30] B. Tripathy and P. Nath, “Statistical convergence of complex uncertain sequences,” New Mathematics and Natural Computation, vol. 13, no. 3, pp. 359–374, 2017. https://doi.org/10.1142/S1793005717500090
[31] B. Das, B. Tripathy, P. Debnath, and B. Bhattacharya, “ Characterization of statistical convergence of complex uncertain double sequence,” Analysis and Mathematical Physics, vol. 10, no. 71, pp. 1–20, 2020. https://doi.org/10.1007/s13324-020-00419-7
[32] O. Kisi and G. E, λ-Statistically Convergence of Complex Uncertain Sequence. CMES, 2019.
[33] O. Kisi, “Sλ(I)-convergence of complex uncertain sequence,” Matematychni Studii, vol. 51, no. 2, pp. 183–194, 2019. https://doi.org/10.15330/ms.51.2.183-194
[34] C. Granados and A. Dhital, “Statistical convergence of double sequences in neutrosophic normed spaces,” Neutrosophic Sets and Systems, vol. 42, pp. 333–344, 2021. http://fs.unm.edu/NSS2/index.php/111/article/view/1294
[2] H. Fast, “ Sur la convergence statistique,” Colloq. Math., vol. 2, no. 1–2, pp. 241–244, 1951. http://eudml.org/doc/209960
[3] B. Liu, “Why is there a need for uncertainty theory?” Journal of Uncertain Systems, vol. 6, no. 1, pp. 3–10, 2012.
[4] I. Schoenberg, “The integrability of certain functions and related summability methods,” Am. Math. Mon., vol. 66, no. 5, pp. 361–375, 1959. https://doi.org/10.1080/00029890.1959.11989303
[5] M. Mursaleen, “λ-statistical convergence,” Math. Slovaca, vol. 50, no. 1, pp. 111–115, 2000. http://eudml.org/doc/34508
[6] P. Kostyrko, M. Macaj, T. Salat, and M. Sleziak, “ I-convergence and extremal I-limit points,” Math. Slovaca, vol. 55, pp. 443–464, 2005.
http://thales.doa.fmph.uniba.sk/sleziak../papers/iconv.pdf
[7] T. Salat, B. Tripathy, and M. Ziman, “On some properties of I-convergence,” Tatra Mt. Math. Publ., vol. 28, pp. 279–286, 2004.
[8] T. Salat, B. C. Tripathy, and M. Ziman, “I-Convergence Field,” Tatra Mt. Math. Publ., vol. 28, pp. 279–286, 2005. http://thales.doa.fmph.uniba.sk/katc/publ/salat_solid.pdf
[9] P. Das, E. Savas, and S. Ghosal, “On generalized of certain summability methods using ideals,” Appl. Math. Letter, vol. 36, no. 9, pp. 1509–1514, 2011. https://doi.org/10.1016/j.aml.2011.03.036
[10] M. Mursaleen and O. Edely, “Statistical convergence of double sequences,” J. Math. Anal. Appl., vol. 288, pp. 223–231, 2003. https://doi.org/10.1016/j.jmaa.2003.08.004
[11] P. Das, P. Kostyrko, W. Wilczynski, and P. Malik, “I and Iλ-convergence of double sequences,” Math. Slovaca, vol. 58, no. 5, pp. 1509–1514, 2008.
[12] B. Liu, Uncertainty Theory Second Edition. Springer-Verlag, 2007. https://doi.org/10.1007/978-3-540-73165-8
[13] B. Liu, Uncertainty Theory: A Branch of Mathematics for Modeling Human Uncertainty. Springer-Verlag, 2011.
[14] B. Liu, Theory and Practice of Uncertain Programming. Springer-Verlag, 2009.
[15] B. Liu and X. Chen, “ Uncertain multiobjective programming and uncertain goal programming,” Journal of Uncertainty Analysis and Applications, vol. 3, pp. 1–10, 2015. https://doi.org/10.1186/s40467-015-0036-6
[16] B. Liu, “Uncertainty risk analysis and uncertain reliability analysis,” Journal of Uncertain Systems, vol. 4, no. 1, pp. 163–170, 2010. http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.1057.5876&rep=rep1&type=pdf
[17] B. Liu, “Uncertainty logic for modelling human language,” Journal of Uncertain Systems, vol. 5, no. 1, pp. 3–20, 2011.
[18] B. Liu, “Fuzzy process, hybrid process and uncertain process,” Journal of Uncertain Systems, vol. 2, no. 1, pp. 3–16, 2008.
[19] K. Yao and X. Chen, “A numerical method for solving uncertain differential equations,” Journal of Intelligent & Fuzzy Systems, vol. 25, no. 3, pp. 825–832, 2013. https://doi.org/10.3233/IFS-120688
[20] X. Gao and Y. Gao, “Connectedness index of uncertain graphs,” International Journal of Uncertainty, Fuzziness & Knowledge-Based Systems, vol. 21, no. 1, pp. 127–137, 2013. https://doi.org/10.1142/S0218488513500074
[21] B. Liu, “ Some research problems in uncertainty theory,” Journal of Uncertain Systems, vol. 3, no. 1, pp. 3–10, 2009. http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.580.3382&rep=rep1&type=pdf
[22] X. Chen, “American option pricing formula for uncertain financial market,” International Journal of Operations Research, vol. 8, no. 2, pp. 32–37, 2011.
[23] B. Liu, “Toward uncertain finance theory,” Journal of Uncertainty Analysis and Applications, vol. 1, pp. 3–16, 2013.
[24] O. Kisi and H. Unal, “ Lacunary statistical convergence of complex uncertain sequence,” Sigma J. Eng. & Nat. Sci., vol. 10, no. 3, pp. 277–286, 2019. https://doi.org/10.5269/bspm.52688
[25] O. Kisi, “The λ-statistically convergent double sequences in fuzzy normed spaces,” hermal Science, vol. 23, no. 1, pp. 153–163, 2019.
[26] O. Kisi, “I2-λ-statistically convergence of double sequences in fuzzy normed spaces,” Journal of Intelligent and Fuzzy Systems, vol. 36, no. 4, pp. 3637–3648, 2019. https://doi.org/10.18514/MMN.2015.821
[27] Z. Peng, Complex uncertain variable. Doctoral Dissertation-Tsinghua University, 2012.
[28] C. You, “On the convergence of uncertain sequences,” Mathematical and Computer Modelling, vol. 49, no. 3–4, pp. 482–487, 2009.
https://doi.org/10.1016/j.mcm.2008.07.007
[29] H. Guo and C. Xu, “A necessary and sufficient condition of convergence in mean square for uncertain sequence,” Information: An International Interdisciplinary Journal, vol. 16, no. 2A, pp. 1091–1096, 2013.
[30] B. Tripathy and P. Nath, “Statistical convergence of complex uncertain sequences,” New Mathematics and Natural Computation, vol. 13, no. 3, pp. 359–374, 2017. https://doi.org/10.1142/S1793005717500090
[31] B. Das, B. Tripathy, P. Debnath, and B. Bhattacharya, “ Characterization of statistical convergence of complex uncertain double sequence,” Analysis and Mathematical Physics, vol. 10, no. 71, pp. 1–20, 2020. https://doi.org/10.1007/s13324-020-00419-7
[32] O. Kisi and G. E, λ-Statistically Convergence of Complex Uncertain Sequence. CMES, 2019.
[33] O. Kisi, “Sλ(I)-convergence of complex uncertain sequence,” Matematychni Studii, vol. 51, no. 2, pp. 183–194, 2019. https://doi.org/10.15330/ms.51.2.183-194
[34] C. Granados and A. Dhital, “Statistical convergence of double sequences in neutrosophic normed spaces,” Neutrosophic Sets and Systems, vol. 42, pp. 333–344, 2021. http://fs.unm.edu/NSS2/index.php/111/article/view/1294
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Published
Dec 1, 2021
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How to Cite
Granados, C. (2021). A Generalized of Sλ-I-Convergence of Complex Uncertain Double Sequences. Ingeniería Y Ciencia, 17(34), 53–75. https://doi.org/10.17230/ingciencia.17.34.3
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