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Strongly Summable Double Sequence Spaces in n-Normed Spaces Defined by Ideal Convergence and an Orlicz Function

  • Esi, Ayhan (Adiyaman University, Science and Art Faculty, Department of Mathematics)
  • Received : 2011.01.09
  • Accepted : 2011.11.24
  • Published : 2012.06.23

Abstract

In this paper we introduce some new double sequence spaces via ideal convergence and an Orlicz function in $n$-normed spaces and examine some properties of the resulting spaces.

Keywords

References

  1. M. Et, Y. Altin, B. Choudhary and B. C. Tripathy, On some classes of sequences defined by sequences of Orlicz functions, Mathematical Inequalities and Applications, 9(2)(2006), 335-342.
  2. S. Gahler, Linear 2-normietre Rume, Math.Nachr., 28(1965), 1-43.
  3. H. Gunawan, On n-inner product, n-norms and the Cauchy-Schwarz Inequality, Scientiae Mathematicae Japonicae Online, 5(2001), 47-54.
  4. H. Gunawan and M. Mashadi, On n-normed spaces, Int. J. Math. & Math. Sci., 27(10)(2001), 631-639. https://doi.org/10.1155/S0161171201010675
  5. P. Kostyrko, T. Salat and W. Wilczynski,I-convergence, Real Analysis Exchange, 26(2)(2000/2001), 669-686.
  6. M. A. Krasnoselski and Y. B. Rutickii, Convex function and Orlicz spaces, Groningen, Nederland, 1961.
  7. I. J. Maddox, Paranormed sequence spaces generated by infinite matrices, Proc. Camb. Phil. Soc., 64(1968), 285-290.
  8. A. Misiak, n-inner product spaces, Math. Nachr., 140(1989), 299-319. https://doi.org/10.1002/mana.19891400121
  9. H. Nakano, Concave modulars, J. Math. Soc. Japan, 5(1953), 29-49. https://doi.org/10.2969/jmsj/00510029
  10. A. Pringsheim, Zur Theori der zweifach unendlichen Zahlenfolgen, Math. Ann. 53(1900), 289-321. https://doi.org/10.1007/BF01448977
  11. D. Rath and B. C. Tripathy, Matrix maps on sequence spaces associated with sets of integers, Indian Jour. Pure Appl. Math., 27(2)(1996), 197-206.
  12. W. H. Ruckle, FK-spaces in which the sequence of coordinate vectors is bounded, Canad. J. Math., 25(1973), 973-978. https://doi.org/10.4153/CJM-1973-102-9
  13. T. Salat, B. C. Tripathy and M. Ziman, On I-convergence field, Italian J. Pure and Appl. Math., 17(2005), 45-54.
  14. S. Simons, The sequence space l ($p_v$)and m($p_v$), Proc. London Math. Soc., 15(3)(1965), 422-436. https://doi.org/10.1112/plms/s3-15.1.422
  15. B. C. Tripathy and B. Hazarika, I-convergent sequence spaces defined by Orlicz function, Acta Mathematica Applicatae Sinica, 27(1)(2001), 149-154.
  16. B. C. Tripathy and M. Sen, On generalized statistically convergent sequences, Indian Jour. Pure Appl. Math., 32(11)(2001), 1689-1694.
  17. B. C. Tripathy, On generalized difference paranormed statistically convergent sequences, Indian Jour. Pure Appl. Math., 35(5)(2004), 655-663.
  18. B. C. Tripathy and S. Mahanta, On a class of generalized lacunary difference sequence spaces defined by Orlicz function, Acta Mathematica Applicatae Sinica, (Eng.Ser.), 20(2)(2004), 231-238. https://doi.org/10.1007/s10255-004-0163-1
  19. B. C. Tripathy and M. Sen, Characterization of some matrix classes involving paranormed sequence spaces, Tamkang Journal of Mathematics, 37(2)(2006), 155-162.
  20. B. C. Tripathy, Y. Altin and M. Et,Generalized difference sequence spaces on seminormed spaces defined by Orlicz functions, Mathematica Slovaca, 58(3)(2008), 315-324. https://doi.org/10.2478/s12175-008-0077-0
  21. B. C. Tripathy and B. Hazarika, I-convergent sequence spaces associated with multiplier sequence spaces, Mathematical Inequalities and Applications, 11(3)(2008), 543-548.
  22. B. C. Tripathy and B. Sarma, Statistically convergent difference double sequence spaces, Acta Mathematica Sinica, 24(5)(2008), 737-742. https://doi.org/10.1007/s10114-007-6648-0
  23. B. C. Tripathy and B. Hazarika, Paranormed I-convergent sequence spaces, Mathematica Slovaca, 59(4)(2009), 485-494. https://doi.org/10.2478/s12175-009-0141-4
  24. B. C. Tripathy and B. Sarma, Vector valued double sequence spaces defined by Orlicz function, Mathematica Slovaca, 59(6)(2009), 767-776. https://doi.org/10.2478/s12175-009-0162-z
  25. B. C. Tripathy and A. J. Dutta, Bounded variation double sequence space of fuzzy real numbers, Computers & Mathematics with Applications, 59(2)(2010), 1031-1037. https://doi.org/10.1016/j.camwa.2009.09.006
  26. B. C. Tripathy and H. Dutta, On some new paranormed difference sequence spaces defined by Orlicz functions, Kyungpook Mathematical Journal, 50(2010), 59-69. https://doi.org/10.5666/KMJ.2010.50.1.059
  27. B. C. Tripathy and S. Mahanta, On I-acceleration convergence of sequences, Journal of the Franklin Institute, 347(2010), 591-598. https://doi.org/10.1016/j.jfranklin.2010.02.001
  28. B. C. Tripathy and P. Chandra, On some generalized paranormed sequence spaces associated with multiplier sequences defined by modulus function, Analysis in Theory and Applications, 27(1)(2011), 21-27. https://doi.org/10.1007/s10496-011-0021-y
  29. B. C. Tripathy and B. Hazarika, I-monotonic and I-convergent sequences, Kyungpook Mathematical Journal, 51(2)(2011), 233-239. https://doi.org/10.5666/KMJ.2011.51.2.233
  30. B. C. Tripathy and B. Sarma, Double sequence spaces of fuzzy numbers defined by Orlicz function, Acta Mathematica Sinica, 31B(1)(2011), 134-140.