대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제27권2호
  • /
  • Pages.399-410
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  • 2012
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  • 1225-1763(pISSN)
  • /
  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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COMMON FIXED POINT THEOREMS UNDER STRICT CONTRACTIVE CONDITIONS IN FUZZY METRIC SPACES USING PROPERTY (E.A)

  • Sedghi, Shaban (Department of Mathematics Qaemshahr Branch Islamic Azad University) ;
  • Shobe, Nabi (Department of Mathematics Islamic Azad University-Babol Branch)
  • 투고 : 2010.12.13
  • 발행 : 2012.04.30
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초록

We prove common fixed point theorems for weakly compatible mappings satisfying strict contractive conditions in fuzzy metric spaces using property (E.A). Our theorems extend a theorem of [1].

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참고문헌

  1. M. Aamri and D. El Moutawakil, Some new common fixed point theorems under strict contractive conditions, J. Math. Anal. Appl. 270 (2002), no. 1, 181-188. https://doi.org/10.1016/S0022-247X(02)00059-8
  2. A. Aliouche, A common fixed point theorem for weakly compatible mappings in symmet- ric spaces satisfying a contractive condition of integral type, J. Math. Anal. Appl. 322 (2006), no. 2, 796-802. https://doi.org/10.1016/j.jmaa.2005.09.068
  3. A. Branciari, A fixed point theorem for mappings satisfying a general contractive condition of integral type, Int. J. Math. Sci. 29 (2002), no. 9, 531-536. https://doi.org/10.1155/S0161171202007524
  4. S. S. Chang, Y. J. Cho, B. S. Lee, J. S. Jung, and S. M. Kang, Coincidence point theorems and minimization theorems in fuzzy metric spaces, Fuzzy Sets and Systems 88 (1997), no. 1, 119-127. https://doi.org/10.1016/S0165-0114(96)00060-7
  5. Y. J. Cho, H. K. Pathak, S. M. Kang, and J. S. Jung, Common fixed points of compatible maps of type (fi) on fuzzy metric spaces, Fuzzy Sets and Systems 93 (1998), no. 1, 99- 111. https://doi.org/10.1016/S0165-0114(96)00200-X
  6. Z. K. Deng, Fuzzy pseudometric spaces, J. Math. Anal. Appl. 86 (1982), no. 1, 74-95. https://doi.org/10.1016/0022-247X(82)90255-4
  7. A. Djoudi and A. Aliouche, Common fixed point theorems of Gregus type for weakly compatible mappings satisfying contractive conditions of integral type, J. Math. Anal. Appl. 329 (2007), no. 1, 31-45. https://doi.org/10.1016/j.jmaa.2006.06.037
  8. M. A. Erceg, Metric spaces in fuzzy set theory, J. Math. Anal. Appl. 69 (1979), no. 1, 205-230. https://doi.org/10.1016/0022-247X(79)90189-6
  9. A. George and P. Veeramani, On some result in fuzzy metric space, Fuzzy Sets and Systems 64 (1994), no. 3, 395-399. https://doi.org/10.1016/0165-0114(94)90162-7
  10. J. Goguen, L-fuzzy sets, J. Math. Anal. Appl. 18 (1967), 145-174. https://doi.org/10.1016/0022-247X(67)90189-8
  11. M. Grebiec, Fixed points in fuzzy metric spaces, Fuzzy Sets and Systems 27 (1988), no. 3, 385-389. https://doi.org/10.1016/0165-0114(88)90064-4
  12. A. Gregori and A. Sapena, On fixed-point theorem in fuzzy metric spaces, Fuzzy Sets and Systems 125 (2002), no. 2, 245-252. https://doi.org/10.1016/S0165-0114(00)00088-9
  13. O. Hadzic, Fixed point theorem for multivalued mappings in probabilistic metric spaces, Fuzzy Sets and Systems 88 (1997), no. 2, 219-226. https://doi.org/10.1016/S0165-0114(96)00072-3
  14. G. Jungck, Compatible mappings and common fixed points, Internat. J. Math. Math. Sci. 9 (1986), no. 4, 771-779. https://doi.org/10.1155/S0161171286000935
  15. O. Kaleva and S. Seikkala, On fuzzy metric spaces, Fuzzy Sets and Systems 12 (1984), no. 3, 215-229. https://doi.org/10.1016/0165-0114(84)90069-1
  16. I. Kramosil and J. Michalek, Fuzzy metric and statistical metric spaces, Kybernetica 11 (1975), no. 5, 326-334.
  17. D. Mihet, A Banach contraction theorem in fuzzy metric spaces, Fuzzy Sets and Systems 144 (2004), no. 3, 431-439. https://doi.org/10.1016/S0165-0114(03)00305-1
  18. R. P. Pant, Common fixed point theorems for contractive maps, J. Math. Anal. Appl. 226 (1998), no. 1, 251-258. https://doi.org/10.1006/jmaa.1998.6029
  19. R. P. Pant, R-weak commutativity and common fixed points, Soochow J. Math. 25 (1999), no. 1, 37-42.
  20. R. P. Pant and V. Pant, Common fixed point under strict contractive conditions, J. Math. Anal. Appl. 248 (2000), no. 1, 327-332. https://doi.org/10.1006/jmaa.2000.6871
  21. E. Pap, O. Hadzic, and R. Mesiar, A fixed point theorem in probabilistic metric spaces and an application, J. Math. Anal. Appl. 202 (1996), no. 2, 433-449. https://doi.org/10.1006/jmaa.1996.0325
  22. J. H. Park, Intuitionistic fuzzy metric spaces, Chaos Solitons Fractals 22 (2004), no. 5, 1039-1046. https://doi.org/10.1016/j.chaos.2004.02.051
  23. B. E. Rhoades, Two fixed-Point Theorems for mappings satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci. 2003 (2003), no. 63, 4007-4013. https://doi.org/10.1155/S0161171203208024
  24. R. Saadati and J. H. Park, On the intuitionistic fuzzy topological spaces, Chaos Solitons Fractals 27 (2006), no. 2, 331-344. https://doi.org/10.1016/j.chaos.2005.03.019
  25. R. Saadati, A. Razani, and H. Adibi, A Common fixed point theorem in L-fuzzy metric spaces, Chaos Solitons Fractals 33 (2007), no. 2, 358-363. https://doi.org/10.1016/j.chaos.2006.01.023
  26. R. Saadati R. and S. Sedghi, A common fixed point theorem for R-weakly commuting maps in fuzzy metric spaces, 6th Iranian Conference on Fuzzy Systems 2006, 387-391.
  27. B. Schweizer and A. Sklar, Probabilistic Metric Spaces, North-Holland, Amsterdam, 1983.
  28. S. Sedghi, N. Shobe, and M. A. Selahshoor, A common fixed point theorem for four mappings in two complete fuzzy metric spaces, Advances in Fuzzy Mathematics 1 (2006), no. 1, 1-8.
  29. P. Vijayaraju, B. E. Rhoades, and R. Mohanraj, A fixed point theorem for a pair of maps satisfying a general contractive condition of integral type, Int. J. Math. Math. Sci. 2005 (2005), no. 15, 2359-2364. https://doi.org/10.1155/IJMMS.2005.2359
  30. L. A. Zadeh, Fuzzy sets, Inform and Control. 8 (1965), 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X