Una generalización de Sλ-I-convergencia de sucesiones dobles complejas inciertas
Main Article Content
Keywords
λI2-convergencia, teoría de la incertidumbre, variable incierta compleja, espacios de ideales
Resumen
En este artículo, se introduce las nociones de sucesiones estadísticamente λI2-convergences las cuales son llamadas estadísticamente λI2-convergence casi seguro (Sλ(I2) c.s.), estadísticamente λI2-convergente en medida, estadísticamente λI2-convergente en media, estadísticamente λI2-convergente en distribución y estadísticamente λI2-convergente uniformemente casi seguro (Sλ(I2) u.c.s.). Adicionalmente, presentamos
algunos teoremas y relaciones existentes entre las nociones mencionadas anteriormente, asu vez, cuando el reciproco de un teorema no se satisface, se presenta un contra ejemplo para soportar el resultado.
Descargas
Los datos de descargas todavía no están disponibles.
Referencias
[1] 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
[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
[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
Article Sidebar
Publicado
dic 1, 2021
Article Details
Cómo citar
Granados, C. (2021). Una generalización de Sλ-I-convergencia de sucesiones dobles complejas inciertas. Ingeniería Y Ciencia, 17(34), 53–75. https://doi.org/10.17230/ingciencia.17.34.3
Número
Sección
Artículos
Agencias de apoyo
No aplica
Esta obra está bajo una licencia internacional Creative Commons Atribución 4.0.
Los autores que publican en esta revista están de acuerdo con los siguientes términos:
- Los autores conservan los derechos de autor y garantizan a la revista el derecho de ser la primera publicación del trabajo al igual que licenciado bajo una Creative Commons Attribution License que permite a otros compartir el trabajo con un reconocimiento de la autoría del trabajo y la publicación inicial en esta revista.
- Los autores pueden establecer por separado acuerdos adicionales para la distribución no exclusiva de la versión de la obra publicada en la revista (por ejemplo, situarlo en un repositorio institucional o publicarlo en un libro), con un reconocimiento de su publicación inicial en esta revista.
- Se permite y se anima a los autores a difundir sus trabajos electrónicamente (por ejemplo, en repositorios institucionales o en su propio sitio web) antes y durante el proceso de envío, ya que puede dar lugar a intercambios productivos, así como a una citación más temprana y mayor de los trabajos publicados (Véase The Effect of Open Access) (en inglés).