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THE DIFFERENCE ORLICZ SPACE OF ENTIRE SEQUENCE OF FUZZY NUMBERS

  • Published : 2010.04.30
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Abstract

In this paper we define and study the difference Orlicz space of entire sequence of fuzzy numbers. We study their different properties and statistical convergence in these spaces.

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References

  1. Y. Altin and M. Et, Generalized difference sequence spaces defined by a modulus function in a locally convex space, Soochow J. Math. 31 (2005), no. 2, 233-243.
  2. S. Aytar, Statistical limit points of sequences of fuzzy numbers, Inform. Sci. 165 (2004), no. 1-2, 129-138. https://doi.org/10.1016/j.ins.2003.06.003
  3. M. Basarir and M. Mursaleen, Some sequence spaces of fuzzy numbers generated by infinite matrices, J. Fuzzy Math. 11 (2003), no. 3, 757-764.
  4. C. Bektas and Y. Altin, The sequence space $l_M$ (p, q, s) on seminormed spaces, Indian J. Pure Appl. Math. 34 (2003), no. 4, 529-534.
  5. T. Bilgin, $\Delta$ - statistical and strong $\Delta$ - Cesaro convergence of sequences of fuzzy numbers, Math. Commun. 8 (2003), no. 1, 95-100.
  6. H. I. Brown, The summability field of a perfect l - l method of summation, J. Analyse Math. 20 (1967), 281-287. https://doi.org/10.1007/BF02786676
  7. R. Colak, M. Et, and E. Malkowsky, Some topics of sequence spaces, Lecture Notes in Mathematics, Firat University Press, Elazig, Turkey, 2004.
  8. P. Diamond and P. Kloeden, Metric spaces of fuzzy sets, Fuzzy Sets and Systems 35 (1990), no. 2, 241-249. https://doi.org/10.1016/0165-0114(90)90197-E
  9. M. Et, On some topological properties of generalized difference sequence spaces, Int. J. Math. Math. Sci. 24 (2000), no. 11, 785-791. https://doi.org/10.1155/S0161171200002325
  10. M. Et and R. Colak, On some generalized difference sequence spaces, Soochow J. Math. 21 (1995), no. 4, 377-386.
  11. J. Fang and H. Huang, On the level convergence of a sequence of fuzzy numbers, Fuzzy Sets and Systems 147 (2004), no. 3, 417-435. https://doi.org/10.1016/j.fss.2003.08.001
  12. H. Fast, Sur la convergence statistique, Colloquium Math. 2 (1951), 241-244.
  13. G. Fricke and R. E. Powell, A theorem on entire methods of summation, Compositio Math. 22 (1970), 253-259.
  14. J. Fridy, On statistical convergence, Analysis 5 (1985), no. 4, 301-313.
  15. C. Goffman and G. Pedrick, First Course in Functional Analysis, Prentice-Hall, Inc., Englewood Cliffs, N.J., 1965.
  16. M. Isik, On statistical convergence of generalized difference sequences, Soochow J. Math. 30 (2004), no. 2, 197-205.
  17. P. K. Kamthan, Bases in a certain class of a Frechet space, Tamkang J. Math. 7 (1976), no. 1, 41-49.
  18. P. K. Kamthan and M. Gupta, Sequence Spaces and Series, Lecture Notes in Pure and Applied Mathematics, 65. Marcel Dekker, Inc., New York, 1981.
  19. H. Kizmaz, On certain sequence spaces, Canad. Math. Bull. 24 (1981), no. 2, 169-176. https://doi.org/10.4153/CMB-1981-027-5
  20. M. A. Krasnosel'skii and Ja. B. Rutickii, Convex Functions and Orlicz Spaces, Translated from the first Russian edition by Leo F. Boron. P. Noordhoff Ltd., Groningen 1961.
  21. J. S. Kwon, On statistical and p-Cesaro convergence of fuzzy numbers, Korean J. Comput. Appl. Math. 7 (2000), no. 1, 195-203.
  22. L. Leindler, Uber die verallgemeinerte de la Vallee-Poussinsche Summierbarkeit allgemeiner Orthogonalreihen, Acta Math. Acad. Sci. Hungar. 16 (1965), 375-387. https://doi.org/10.1007/BF01904844
  23. J. Lindenstrauss and L. Tzafriri, On Orlicz sequence spaces, Israel J. Math. 10 (1971), 379-390. https://doi.org/10.1007/BF02771656
  24. I. J. Maddox, Elements of Functional Analysis, Cambridge University Press, London- New York, 1970.
  25. I. J. Maddox, Sequence spaces defined by a modulus, Math. Proc. Cambridge Philos. Soc. 100 (1986), no. 1, 161-166. https://doi.org/10.1017/S0305004100065968
  26. M. Matloka, Sequences of fuzzy numbers, Busefal 28 (1986), 28-37.
  27. E. T. Mikail and F. Nuray, ${\Delta}^m$-statistical convergence, Indian J. Pure Appl. Math. 32 (2001), no. 6, 961-969.
  28. M. Mursaleen and M. Basarir, On some new sequence spaces of fuzzy numbers, Indian J. Pure Appl. Math. 34 (2003), no. 9, 1351-1357.
  29. M. Mursaleen, M. A. Khan, and Qamaruddin, Difference sequence spaces defined by Orlicz functions, Demonstratio Math. 32 (1999), no. 1, 145-150.
  30. H. Nakano, Concave modulars, J. Math. Soc. Japan 5 (1953), 29-49. https://doi.org/10.2969/jmsj/00510029
  31. S. Nanda, On sequences of fuzzy numbers, Fuzzy Sets and Systems 33 (1989), no. 1, 123-126. https://doi.org/10.1016/0165-0114(89)90222-4
  32. I. Niven and H. S. Zuckerman, An Introduction to the Theory of Numbers, Fourth ed., John Wiley and Sons, New York, 1980.
  33. F. Nuray, Lacunary statistical convergence of sequences of fuzzy numbers, Fuzzy Sets and Systems 99 (1998), no. 3, 353-355. https://doi.org/10.1016/S0165-0114(98)00031-1
  34. F. Nuray and E. Savas, Statistical convergence of sequences of fuzzy numbers, Math. Slovaca 45 (1995), no. 3, 269-273.
  35. W. Orlicz, ber Raume $(L^M)$, Bull. Internat. Acad. Polon. Sci. Lett. Cl. Sci. Math. Nat. Ser. A (1936), 93-107.
  36. S. D. Parashar and B. Choudhary, Sequence spaces defined by Orlicz functions, Indian J. Pure Appl. Math. 25 (1994), no. 4, 419-428.
  37. K. Chandrasekhara Rao and N. Subramanian, The Orlicz space of entire sequences, Int. J. Math. Math. Sci. 2004 (2004), no. 65-68, 3755-3764. https://doi.org/10.1155/S0161171204311385
  38. K. Chandrasekhara Rao and T. G. Srinivasalu, Matrix operators on analytic and entire sequences, Bull. Malaysian Math. Soc. (2) 14 (1991), no. 1, 41-54.
  39. 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
  40. E. Savas, On strongly $\lambda$-summable sequences of fuzzy numbers, Inform. Sci. 125 (2000), no. 1-4, 181-186. https://doi.org/10.1016/S0020-0255(99)00151-6
  41. I. J. Schoenberg, The integrability of certain functions and related summability methods, Amer. Math. Monthly 66 (1959), 361-375. https://doi.org/10.2307/2308747
  42. B. C. Tripathy, M. Et, and Y. Altin, Generalized difference sequence spaces defined by Orlicz function in a locally convex space, J. Anal. Appl. 1 (2003), no. 3, 175-192.
  43. A. Wilansky, Summability through Functional Analysis, North-Holland Mathematics Studies, 85. Notas de Matematica [Mathematical Notes], 91. North-Holland Publishing Co., Amsterdam, 1984.
  44. C. Wu and G. Wang, Convergence of sequences of fuzzy numbers and fixed point theorems for increasing fuzzy mappings and application, Fuzzy Sets and Systems 130 (2002), no. 3, 383-930. https://doi.org/10.1016/S0165-0114(01)00231-7
  45. L. A. Zadeh, Fuzzy sets, Information and Control 8 (1965), 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X