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Sequence Space m(M, φ)F of Fuzzy Real Numbers Defined by Orlicz Functions with Fuzzy Metric

  • Tripathy, Binod Chandra (Mathematical Sciences Division, Institute of Advanced Study in Science and Technology) ;
  • Borgohain, Stuti (Mathematical Sciences Division, Institute of Advanced Study in Science and Technology)
  • Received : 2011.03.08
  • Accepted : 2011.09.23
  • Published : 2013.09.23

Abstract

The sequence space $m(M,{\phi})^F$ of fuzzy real numbers is introduced. Some properties of this sequence space like solidness, symmetricity, convergence-free etc. are studied. We obtain some inclusion relations involving this sequence space.

Keywords

References

  1. Y. Altin, M. Et and B. C. Tripathy, The sequence space on seminormed spaces, Applied Math. Computation, 154(2004), 423-430. https://doi.org/10.1016/S0096-3003(03)00722-7
  2. A. Esi, On some new paranormed sequence spaces of fuzzy numbers defined by Orlicz functions and statistical convergence, Math. Model. Anal., 11(2006), 379-388.
  3. M. Et, Y. Altin, B. Choudhary and B. C. Tripathy, On some classes of sequences defined by sequences of Orlicz functions, Math. Ineq. Appl., 9(2)(2006),335-342.
  4. O. Kaleva and S. Seikkala, On fuzzy metric spaces, Fuzzy Sets Syst., 12(1984), 215-229. https://doi.org/10.1016/0165-0114(84)90069-1
  5. J. Lindenstrauss and L. Tzafriri, On Orlicz sequence spaces, Israel J. Math., 10(1971), 379-390. https://doi.org/10.1007/BF02771656
  6. F. Nuray and E. Savas, Statistical convergence of sequences of fuzzy real numbers, Math. Slovaca, 45(3)(1995), 269-273.
  7. D. Rath and B. C. Tripathy, Characterization of certain matrix operators, J. Orissa Math Soc, 8(1989), 121-134.
  8. W. L. C. Sargent, Some sequence spaces related to spaces, J. Lond. Math. Soc., 35(1960), 161-171.
  9. Y. Syau, Sequences in a fuzzy metric space, Computer Math. Appl., 33(6)(1997), 73-76.
  10. B. C. Tripathy, Matrix maps on the power series convergent on the unit disc, J. Analysis, 6(1998), 27-31.
  11. B. C. Tripathy, A class of difference sequences related to the p-normed space ${\ell}_{p}$, Demonstratio Math., 36(4)(2003), 867-872.
  12. B. C. Tripathy, A. Altin and M. Et, Generalized difference sequences spaces on seminormed spaces defined by Orlicz functions, Math. Slovaca, 58(3)(2008), 315-324 https://doi.org/10.2478/s12175-008-0077-0
  13. B. C. Tripathy and A. Baruah, Lacunary statistically convergent and lacunary strongly convergent generalized difference sequences of fuzzy real numbers, Kyungpook Math. J., 50(2010), 565-574. https://doi.org/10.5666/KMJ.2010.50.4.565
  14. B. C. Tripathy and A. Baruah, Norlund and Riesz mean of sequences of fuzzy real numbers, Appl. Math. Lett., 23(2010), 651-655. https://doi.org/10.1016/j.aml.2010.02.006
  15. B. C. Tripathy and A. Baruah, New type of difference sequence spaces of fuzzy real numbers, Math. Model. Anal., 14(3)(2009), 391-397. https://doi.org/10.3846/1392-6292.2009.14.391-397
  16. B. C. Tripathy and S. Borgohain, The sequence space $m(M,{\phi}.{\Delta}^{n}_{m},p)^{F}$, Math. Model. Anal., 13(4)(2008), 577-586. https://doi.org/10.3846/1392-6292.2008.13.577-586
  17. B. C. Tripathy and A. J. Dutta, On fuzzy real-valued double sequence spaces, Math. Comput. Model., 46(9-10)(2007), 1294-1299. https://doi.org/10.1016/j.mcm.2007.01.006
  18. B. C. Tripathy and A. J. Dutta, Bounded variation double sequence space of fuzzy real numbers, Computers Math. Appl., 59(2)(2010), 1031-1037. https://doi.org/10.1016/j.camwa.2009.09.006
  19. B. C. Tripathy and S. Mahanta, On a class of generalized lacunary difference sequence spaces defined by Orlicz function, Acta Math. Appl. Sin.(Eng. Ser.), 20(2)(2004), 231-238. https://doi.org/10.1007/s10255-004-0163-1
  20. B. C. Tripathy and B. Sarma, Sequence spaces of fuzzy real numbers defined by Orlicz functions, Math. Slovaca, 58(5)(2008), 621-628. https://doi.org/10.2478/s12175-008-0097-9
  21. B. C. Tripathy and B. Sarma, Vector valued double sequence spaces defined by Orlicz function, Math. Slovaca, 59(6)(2009), 767-776. https://doi.org/10.2478/s12175-009-0162-z

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