A Generalized of Sλ-I-Convergence of Complex Uncertain Double Sequences
DOI:
https://doi.org/10.17230/ingciencia.17.34.3Keywords:
λI2-convergence, uncertainty theory, complex uncertain variable, ideal spacesAbstract
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.
Downloads
References
A. Freedman and J. Sember, “Densities and summability,” Pac. J. Math., vol. 95, no. 2, pp. 293–305, 1981. https://doi.org/10.2140/pjm.1981.95.293
H. Fast, “ Sur la convergence statistique,” Colloq. Math., vol. 2, no. 1–2, pp. 241–244, 1951. http://eudml.org/doc/209960
B. Liu, “Why is there a need for uncertainty theory?” Journal of Uncertain Systems, vol. 6, no. 1, pp. 3–10, 2012.
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
M. Mursaleen, “λ-statistical convergence,” Math. Slovaca, vol. 50, no. 1, pp. 111–115, 2000. http://eudml.org/doc/34508
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
T. Salat, B. Tripathy, and M. Ziman, “On some properties of I-convergence,” Tatra Mt. Math. Publ., vol. 28, pp. 279–286, 2004.
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
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
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
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.
B. Liu, Uncertainty Theory Second Edition. Springer-Verlag, 2007. https://doi.org/10.1007/978-3-540-73165-8
B. Liu, Uncertainty Theory: A Branch of Mathematics for Modeling Human Uncertainty. Springer-Verlag, 2011.
B. Liu, Theory and Practice of Uncertain Programming. Springer-Verlag, 2009.
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
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
B. Liu, “Uncertainty logic for modelling human language,” Journal of Uncertain Systems, vol. 5, no. 1, pp. 3–20, 2011.
B. Liu, “Fuzzy process, hybrid process and uncertain process,” Journal of Uncertain Systems, vol. 2, no. 1, pp. 3–16, 2008.
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
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
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
X. Chen, “American option pricing formula for uncertain financial market,” International Journal of Operations Research, vol. 8, no. 2, pp. 32–37, 2011.
B. Liu, “Toward uncertain finance theory,” Journal of Uncertainty Analysis and Applications, vol. 1, pp. 3–16, 2013.
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
O. Kisi, “The λ-statistically convergent double sequences in fuzzy normed spaces,” hermal Science, vol. 23, no. 1, pp. 153–163, 2019.
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
Z. Peng, Complex uncertain variable. Doctoral Dissertation-Tsinghua University, 2012.
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
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.
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
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
O. Kisi and G. E, λ-Statistically Convergence of Complex Uncertain Sequence. CMES, 2019.
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
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
Downloads
Published
Issue
Section
License
Copyright (c) 2021 Carlos Granados
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
Plagiarism Detection