Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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On Paranormed Type Fuzzy Real Valued Class of Sequences 2ℓF(p)

  • Sen, Mausumi (Department of Mathematics, National Institute of Tecgnology) ;
  • Roy, Santanu (Department of Mathematics, National Institute of Tecgnology)
  • Received : 2010.09.13
  • Accepted : 2011.01.20
  • Published : 2011.09.23
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Abstract

In this article we introduce the fuzzy real valued double sequence spaces $_2{\ell}^F$ (p) where p = ($p_{nk}$) is a double sequence of bounded strictly positive numbers. We study their different properties like completeness, solidness, symmetricity, convergence free etc. We prove some inclusion results also.

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References

  1. T. J. I'A Bromaich, An Introduction to the Theory of Infinite Series, Macmillan & Co. Ltd., New York, 1965.
  2. B. Choudhury, and B. C. Tripathy, On fuzzy real valued ${\ell}(p)^F$ sequence spaces, Proc International Conference, held at Salt Lake city, USA, during July 21-25(2005), 184-190.
  3. G. H. Hardy, On the convergence of certain multiple series, Proc. Camb Phil. Soc., 19(1917), 86-95.
  4. O. Kaleva and O. Kaleva, On fuzzy metric spaces, Fuzzy Sets and Systems, 12(1984), 215-229. https://doi.org/10.1016/0165-0114(84)90069-1
  5. S. Nanda, On sequences of fuzzy numbers, Fuzzy Sets and Systems, 33(1989), 123-126. https://doi.org/10.1016/0165-0114(89)90222-4
  6. F. Nuray and E. Savas, Statistical convergence of sequences of fuzzy real numbers, Math. Slovaca, 45(3)(1995), 269-273.
  7. B. C. Tripathy, On generalized difference paranormed statistically convergent sequences, Indian Journal of Pure and Applied Mathematics, 35(5)(2004), 655-663.
  8. B. C. Tripathy and A. Baruah, New type of difference sequence spaces of fuzzy real numbers, Mathematical Modelling and Analysis, 14(3)(2009), 391-397. https://doi.org/10.3846/1392-6292.2009.14.391-397
  9. B. C. Tripathy and A. Baruah, Norlund and Riesz mean of sequences of fuzzy real numbers, Applied Mathematics Letters, 23(2010), 651-655. https://doi.org/10.1016/j.aml.2010.02.006
  10. B. C. Tripathy and A. J. Dutta, Bounded variation double sequence space of fuzzy real numbers, Computers & Mathematics with Applications. 9(2)(2010), 1031-1037.
  11. B. C. Tripathy and A. J. Dutta, On fuzzy real valued double sequence spaces, Soochow jour. Of Math., 32(4)(2006), 509-520.
  12. B. C. Tripathy and A. J. Dutta, On fuzzy real valued double sequence spaces $2{\ell}^p_F$ , Mathematical and Computer, 46(2007), 1294-1299.
  13. 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
  14. 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
  15. B. C. Tripathy and B. Sarma, Sequence spaces of fuzzy real numbers defined by Orlicz functions, Mathematica Slovaca, 58(5)(2008), 621-628. https://doi.org/10.2478/s12175-008-0097-9
  16. B. C. Tripathy and M. Sen, On generalized statistically convergent sequences, Indian Journal of Pure and Applied Mathematics, 32(11)(2001), 1689-1694.
  17. B. C. Tripathy and M. Sen, Characterization of some matrix classes involving paranormed sequence spaces, Tamkang Journal of Mathematics, 37(2)(2006), 155-162.
  18. B. C. Tripathy, and S. Borgohain, The sequence space $m(M,\phi,{\Delta}^n_m,p)^F$ , Mathematical Modelling and Analysis, 13(4)(2008), 577-586. https://doi.org/10.3846/1392-6292.2008.13.577-586
  19. L. A. Zadeh, Fuzzy sets,, Information and Control, 8(1965), 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X