I-Pre- Cauchy Triple sequences of Fuzzy Number and Double Orlicz functions
DOI:
https://doi.org/10.29304/jqcm.2023.15.1.1190Keywords:
filter, Paranorm; Ideal, ; Invariant Mean, I-convergent, Monotone and solid space.Abstract
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References
[1] J. Connor, J.A. Fridy & J. Kline, "Statistically Pre-Cauchy Sequence," Analysis, Vol. 14, 1994, pp. 311-317.
[2] A. K. Vakeel & Q. M. Danish Lohani, “Statistically Pre-Cauchy Sequences and Orlicz Functions," Southeast Asian Bulletin of Mathematics, Vol.
31, No. 6, 2007, pp. 1107-1112.
[3] H. Steinhaus, "Sur la Convergence Ordinaire et la Con-vergence Asymptotique," Colloquium Mathematicum, Vol. 2, 1951, pp. 73-74.
[4] H. Fast, "Sur la Convergence Statistique," Colloquium Mathematicum, Vol. 2, 1951, pp. 241-244.
[5] R.C. Buck, "Generalized Asymptotic Density," American Journal of Mathematics, Vol. 75, No. 2, 1953, pp. 335-346
[6] 1.J. Schoenberg, "The Integrability of Certain Functions and Related Summability Methods," The American Mathematical Monthly, Vol. 66, 1959,
pp. 361-375.
[7] T.Salat, "On Statistically Convergent Sequences of Real Numbers," Mathematica Slovaca, Vol. 30, 1980, pp. 139-150.
[8] J. A. Fridy, "On Statistical Convergence," Analysis, Vol 5, 1985, pp. 301-311.
[9] J. S. Connor, "The Statistical and Strong P-Cesaro Con-vergence of Sequences," Analysis, Vol. 8, 1988, pp. 47-63.
[10] M. Gurdal, "Statistically Pre-Cauchy Sequences and Bounded Moduli," Acta et Commentationes Universitatis Tarytensis de Mathematica, Vol. 7,
2003, pp. 3-7.
[11] T.J.I. Bromwich, "An Introduction to the Theory of Infinite Series," MacMillan and Co. Ltd., New York, 1965.
[12] B.C. Tripathy, "Statistically Convergent Double Sequen-ces," Tamkang Journal of Mathematics, Vol. 32, No. 2, 2006, pp. 211-221.
[13] M. Basarir & O. Solancan, "On Some Double Seuence Spaces," The Journal of The Indian Academy of Mathematics, Vol. 21, No. 2, 1999, pp.
193-200.
[14] 1. J. Maddox, "Elements of Functional Analysis," Cambridge University Press, Cambridge, Cambridge, 1970.
[15] J. Lindenstrauss & L. Tzafriri, "On Orlicz Sequence Spaces," Israel Journal of Mathematics, Vol. 10, No. 3, 1971, pp. 379-390.
doi:10.1007/BF02771656
[16] M. Et, "On Some New Orlicz Sequence Spaces," Journal of Analysis, Vol. 9, 2001, pp. 21-28.
[17] S.D. Parashar & B. Choudhary, "Sequence Spaces Defined by Orlicz Function," Indian Journal of Pure and Applied Mathematics, Vol. 25, 1994, pp.
419 428.
[18] B.C. Tripathy & Mahantas, "On a Class of Sequences Related to the 1P Space Defined by the Orlicz Functions," Soochow Journal of Mathematics, Vol.
29, No. 4, 2003, pp. 379-391.
[19] A. K. Vakeel & S. Tabassum, "Statistically Pre-Cauchy Double Sequences and Orlicz Functions," Southeast Asian Bulletin of Mathematics, Vol.
36, No. 2, 2012, pp. 249-254.
[20] A. K. Vakeel, K. Ebadullah & A Ahmad, "I-Pre-Cauchy Sequences and Orlicz Functions." Journal of Mathemati cal Analysis, Vol. 3, No. 1, 2012,
pp. 21-26.
[21] P. Kostyrko, T. Salat & W. Wilczynski, "I-Conver gence," Real Analysis Exchange, Vol. 26, No. 2, 2000, pp. 669-686.
[22] T. Salat, B.C. Tripathy & M. Ziman, "On Some Prop erties of I-Convergence," Tatra Mountains Mathematical Publications, Vol. 28, 2004, pp.
279-286.
[23] K. Demirci, “I-Limit Superior and Limit Inferior," Ma thematical Communications, Vol. 6, 2001, pp. 165-172.
[24] B.C. Tripathy & B. Hazarika, "Paranorm I-Convergent Sequence Spaces," Mathematica Slovaca, Vol. 59, No. 4, 2009, pp. 485-494.
doi:10.2478/s12175-009-0141-4
[25] B.C. Tripathy & B. Hazarika, "Some 1-Convergent Sequence Spaces Defined by Orlicz Function," Acta Mathe- matica Applicatae Sinica, Vol. 27,
No. 1, 2011, pp. 149-154. doi:10.1007/s10255-011-0048-z
[26] B.C. Tripathy & B. Hazarika, "I-Monotonic and I-Convergent Sequences,” Kyungpook Mathematical Journal, Vol. 51, No. 2, 2011, pp. 233-239.
doi:10.5666/KMJ.2011.51.2.233
[27] A. K. Vakeel, K. Ebadullah & S. Suthep, "On a New I-Convergent Sequence Spaces," Analysis, Vol. 32, No. 3, 2012, pp. 199-208.
doi:10.1524/anly.2012.1148
[28] M. Gurdal & M. B. Huban, “On I-Convergence of Double Sequences in the Topology induced by Random 2Norms," Matematicki Vesnik, Vol. 65,
No. 3, 2013, pp. 1-13.
[2] A. K. Vakeel & Q. M. Danish Lohani, “Statistically Pre-Cauchy Sequences and Orlicz Functions," Southeast Asian Bulletin of Mathematics, Vol.
31, No. 6, 2007, pp. 1107-1112.
[3] H. Steinhaus, "Sur la Convergence Ordinaire et la Con-vergence Asymptotique," Colloquium Mathematicum, Vol. 2, 1951, pp. 73-74.
[4] H. Fast, "Sur la Convergence Statistique," Colloquium Mathematicum, Vol. 2, 1951, pp. 241-244.
[5] R.C. Buck, "Generalized Asymptotic Density," American Journal of Mathematics, Vol. 75, No. 2, 1953, pp. 335-346
[6] 1.J. Schoenberg, "The Integrability of Certain Functions and Related Summability Methods," The American Mathematical Monthly, Vol. 66, 1959,
pp. 361-375.
[7] T.Salat, "On Statistically Convergent Sequences of Real Numbers," Mathematica Slovaca, Vol. 30, 1980, pp. 139-150.
[8] J. A. Fridy, "On Statistical Convergence," Analysis, Vol 5, 1985, pp. 301-311.
[9] J. S. Connor, "The Statistical and Strong P-Cesaro Con-vergence of Sequences," Analysis, Vol. 8, 1988, pp. 47-63.
[10] M. Gurdal, "Statistically Pre-Cauchy Sequences and Bounded Moduli," Acta et Commentationes Universitatis Tarytensis de Mathematica, Vol. 7,
2003, pp. 3-7.
[11] T.J.I. Bromwich, "An Introduction to the Theory of Infinite Series," MacMillan and Co. Ltd., New York, 1965.
[12] B.C. Tripathy, "Statistically Convergent Double Sequen-ces," Tamkang Journal of Mathematics, Vol. 32, No. 2, 2006, pp. 211-221.
[13] M. Basarir & O. Solancan, "On Some Double Seuence Spaces," The Journal of The Indian Academy of Mathematics, Vol. 21, No. 2, 1999, pp.
193-200.
[14] 1. J. Maddox, "Elements of Functional Analysis," Cambridge University Press, Cambridge, Cambridge, 1970.
[15] J. Lindenstrauss & L. Tzafriri, "On Orlicz Sequence Spaces," Israel Journal of Mathematics, Vol. 10, No. 3, 1971, pp. 379-390.
doi:10.1007/BF02771656
[16] M. Et, "On Some New Orlicz Sequence Spaces," Journal of Analysis, Vol. 9, 2001, pp. 21-28.
[17] S.D. Parashar & B. Choudhary, "Sequence Spaces Defined by Orlicz Function," Indian Journal of Pure and Applied Mathematics, Vol. 25, 1994, pp.
419 428.
[18] B.C. Tripathy & Mahantas, "On a Class of Sequences Related to the 1P Space Defined by the Orlicz Functions," Soochow Journal of Mathematics, Vol.
29, No. 4, 2003, pp. 379-391.
[19] A. K. Vakeel & S. Tabassum, "Statistically Pre-Cauchy Double Sequences and Orlicz Functions," Southeast Asian Bulletin of Mathematics, Vol.
36, No. 2, 2012, pp. 249-254.
[20] A. K. Vakeel, K. Ebadullah & A Ahmad, "I-Pre-Cauchy Sequences and Orlicz Functions." Journal of Mathemati cal Analysis, Vol. 3, No. 1, 2012,
pp. 21-26.
[21] P. Kostyrko, T. Salat & W. Wilczynski, "I-Conver gence," Real Analysis Exchange, Vol. 26, No. 2, 2000, pp. 669-686.
[22] T. Salat, B.C. Tripathy & M. Ziman, "On Some Prop erties of I-Convergence," Tatra Mountains Mathematical Publications, Vol. 28, 2004, pp.
279-286.
[23] K. Demirci, “I-Limit Superior and Limit Inferior," Ma thematical Communications, Vol. 6, 2001, pp. 165-172.
[24] B.C. Tripathy & B. Hazarika, "Paranorm I-Convergent Sequence Spaces," Mathematica Slovaca, Vol. 59, No. 4, 2009, pp. 485-494.
doi:10.2478/s12175-009-0141-4
[25] B.C. Tripathy & B. Hazarika, "Some 1-Convergent Sequence Spaces Defined by Orlicz Function," Acta Mathe- matica Applicatae Sinica, Vol. 27,
No. 1, 2011, pp. 149-154. doi:10.1007/s10255-011-0048-z
[26] B.C. Tripathy & B. Hazarika, "I-Monotonic and I-Convergent Sequences,” Kyungpook Mathematical Journal, Vol. 51, No. 2, 2011, pp. 233-239.
doi:10.5666/KMJ.2011.51.2.233
[27] A. K. Vakeel, K. Ebadullah & S. Suthep, "On a New I-Convergent Sequence Spaces," Analysis, Vol. 32, No. 3, 2012, pp. 199-208.
doi:10.1524/anly.2012.1148
[28] M. Gurdal & M. B. Huban, “On I-Convergence of Double Sequences in the Topology induced by Random 2Norms," Matematicki Vesnik, Vol. 65,
No. 3, 2013, pp. 1-13.
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Published
2023-04-11
How to Cite
Abd Al-Hussein, T. M., & Battor, A. H. (2023). I-Pre- Cauchy Triple sequences of Fuzzy Number and Double Orlicz functions. Journal of Al-Qadisiyah for Computer Science and Mathematics, 15(1), Math Page 174–180. https://doi.org/10.29304/jqcm.2023.15.1.1190
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