I-Pre-Cauchy Double Sequences and Orlicz Functions

Show more

References

[1] J. Connor, J. A. Fridy and J. Kline, “Statistically PreCauchy Sequence,” Analysis, Vol. 14, 1994, pp. 311-317.

[2] A. K. Vakeel and 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 Convergence 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. 335346.

[6] I. 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. 139150.

[8] J. A. Fridy, “On Statistical Convergence,” Analysis, Vol 5, 1985, pp. 301-311.

[9] J. S. Connor, “The Statistical and Strong P-Cesaro Convergence of Sequences,” Analysis, Vol. 8, 1988, pp. 4763.

[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 Sequences,” Tamkang Journal of Mathematics, Vol. 32, No. 2, 2006, pp. 211-221.

[13] M. Basarir and O. Solancan, “On Some Double Seuence Spaces,” The Journal of The Indian Academy of Mathematics, Vol. 21, No. 2, 1999, pp. 193-200.

[14] I. J. Maddox, “Elements of Functional Analysis,” Cambridge University Press, Cambridge, Cambridge, 1970.

[15] J. Lindenstrauss and 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 and 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 and Mahantas, “On a Class of Sequences Related to the lp Space Defined by the Orlicz Functions,” Soochow Journal of Mathematics, Vol. 29, No. 4, 2003, pp. 379-391.

[19] A. K. Vakeel and 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 and A Ahmad, “I-Pre-Cauchy Sequences and Orlicz Functions,” Journal of Mathematical Analysis, Vol. 3, No. 1, 2012, pp. 21-26.

[21] P. Kostyrko, T. Salat and W. Wilczynski, “I-Convergence,” Real Analysis Exchange, Vol. 26, No. 2, 2000, pp. 669-686.

[22] T. Salat, B. C. Tripathy and M. Ziman, “On Some Properties of I-Convergence,” Tatra Mountains Mathematical Publications, Vol. 28, 2004, pp. 279-286.

[23] K. Demirci, “I-Limit Superior and Limit Inferior,” Mathematical Communications, Vol. 6, 2001, pp. 165-172.

[24] B. C. Tripathy and 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 and B. Hazarika, “Some I-Convergent Sequence Spaces Defined by Orlicz Function,” Acta Mathematica Applicatae Sinica, Vol. 27, No. 1, 2011, pp. 149154. doi:10.1007/s10255-011-0048-z

[26] B. C. Tripathy and 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 and 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 and 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.