Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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COMPATIBLE MAPPINGS OF TYPE (I) AND (II) ON INTUITIONISTIC FUZZY METRIC SPACES IN CONSIDERATION OF COMMON FIXED POINT

  • Published : 2009.04.30

Abstract

In this paper, we formulate the definition of compatible mappings of type (I) and (II) in intuitionistic fuzzy metric spaces and prove a common fixed point theorem by using the conditions of compatible mappings of type (I) and (II) in complete intuitionistic fuzzy metric spaces. Our results intuitionistically fuzzify the result of Cho, Sedghi, and Shobe [4].

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References

  1. C. Alaca, D. Turkoglu, and C. Yildiz, Fixed points in intuitionistic fuzzy metric spaces, Chaos, Solitons and Frectals 29 (2006), 1073–1078 https://doi.org/10.1016/j.chaos.2005.08.066
  2. K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems 20 (1986), 87–96 https://doi.org/10.1016/S0165-0114(86)80034-3
  3. S. Banach, Theoriles operations Linearies Manograie Mathematyezne, Warsaw, Poland
  4. Y. J. Cho, S. Sedghi, and N. Shobe, Generalized fixed point theorems for compatible mappings with some types in fuzzy metric spaces, Chaos Solitons and Fractals, article in press https://doi.org/10.1016/j.chaos.2007.06.108
  5. D. Dubois and H. Prade, Fuzzy Sets: theory and applications to policy analysis and informations systems, Plnum Press. New York, 1980
  6. M. Edelstein, On fixed and periodic points under contractive mappings, J. London Math. Soc. 37 (1962), 74–79 https://doi.org/10.1112/jlms/s1-37.1.74
  7. MS. El Naschie, On the uncertainty of cantorian geometry and two-slit experiment, Chaos, Solitons and Fractals 9 (1998), 517–529 https://doi.org/10.1016/S0960-0779(97)00150-1
  8. MS. El Naschie, On the verification of heterotic strings theory and e(1) theory, Chaos, Solitons and Fractals 11 (2000), 2397–2408 https://doi.org/10.1016/S0960-0779(00)00108-9
  9. MS. El Naschie, The two slit experiment as the foundation of E-infinity of high energy physics, Chaos, Solitions and Fractals 25 (2005), 509–514 https://doi.org/10.1016/j.chaos.2005.02.016
  10. MS. El Naschie, 'tHooft ultimate building blocks and space-time an infinite dimensional set of transfinite discrete points, Chaos, Solitons and Fractals 25 (2005), 521–524 https://doi.org/10.1016/j.chaos.2005.01.022
  11. A. George and P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets and Systems 64 (1994), 395–399 https://doi.org/10.1016/0165-0114(94)90162-7
  12. M. Grabiec, Fixed points in fuzzy metric spaces, Fuzzy Sets and System 27 (1988), 385–389 https://doi.org/10.1016/0165-0114(88)90064-4
  13. V. Gregory, S. Romaguera, and P. Veeramani, A note on intuitionistic fuzzy metric spaces, Chaos, Solitions and Fractals 28 (2006), 902–905 https://doi.org/10.1016/j.chaos.2005.08.113
  14. G. Jungck, Commuting maps and fixed points, Amer Math Monthly 83 (1976), 261–263 https://doi.org/10.2307/2318216
  15. G. Jungck, Compatible mappings and common fixed point, Int. J. Math. Math. Sci. 9 (1986), 771–779 https://doi.org/10.1155/S0161171286000935
  16. G. Jungck, P. P. Murthy, and Y. J. Cho, Compatible mappings of type (A) and common fixed points, Math. Jponica 38 (1993), 381–390
  17. E. P. Klement, Operations on fuzzy sets an axiomatic approach, Information Science 27 (1984), 221–232 https://doi.org/10.1016/0020-0255(82)90026-3
  18. E. P. Klement, R. Mesiar, and E. Pap, Triangular Norm, Kluwer Academic Pub. Trends in logic 8, Dordrecnt 2000
  19. O. Kramosil and J. Michalek, Fuzzy metric and statistical metric spaces, Kybernetica 11 (1975), 326–334
  20. R. Lowen, Fuzzy Set Theory, Kluwer, Academic Pub. Dordrecht, 1996
  21. K. Menger, Statistical metric, Proc. Nat. Acad. Sci. 28 (1942), 535–537 https://doi.org/10.1073/pnas.28.12.535
  22. J. H. Park, Intuitionistic fuzzy metric spaces, Chaos, Solitions and Fractals 22 (2004), 1039–1046 https://doi.org/10.1016/j.chaos.2004.02.051
  23. H. K. Pathak, Y. J. Cho, and S. M. Kang, Compatible mappings of type (P) and fixed point theorems in metric spaces and probabilistic metric spaces, Novi Sad J. Math. 26 (1996), 87–109
  24. H. K. Pathak, N. Mishra, and A. K. Kalinde, Common fixed point theorems with applications to nonlinear integral equation, Demonstratio Math 32 (1999), 517–564
  25. J. L. Rodriguez and S. Ramagurea, The Hausdorff fuzzy metric on compact sets, Fuzzy Set System 147 (2004), 273–283 https://doi.org/10.1016/j.fss.2003.09.007
  26. R. Sadati and J. H. Park, On the intuitionistic topological spaces, Chaos, Solutions and Fractals 27 (2006), 331–344 https://doi.org/10.1016/j.chaos.2005.03.019
  27. B. Schweizer and A Sklar, Statistical metric spaces, Pacific J Math. 10 (1960), 314–334
  28. S. Sessa, On some weak commutativity condition of mappings in fixed point consideration, Publ. Inst. Math. (Beograd) 32 (1982), 149–153
  29. S. Sharma and B. Deshpande, Common fixed point theorems for finite number of mappings without continuity and compatibility on intuitionistic fuzzy metric spaces, Chaos Solitons and Fractals, article in press https://doi.org/10.1016/j.chaos.2007.10.011
  30. D. Turkoglu, C. Alaca, Y. J. Cho, and C. Yildiz, Common fixed point theorems in intuitionistic fuzzy metric spaces, J. Appl. Math. and Computing 22 (2006), no. 1-2, 411–424 https://doi.org/10.1007/BF02896489
  31. R. R. Yager, On a class of weak triangular norm operators, Information Sciences 96 (1997), no. 1-2, 47–78 https://doi.org/10.1016/S0020-0255(96)00140-5

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