Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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SOME FIXED POINT THEOREMS ON FUZZY METRIC SPACES WITH IMPLICIT RELATIONS

  • Altun, Ishak (DEPARTMENT OF MATHEMATICS FACULTY OF SCIENCE AND ARTS KIRKKALE UNIVERSITY) ;
  • Turkoglu, Duran (DEPARTMENT OF MATHEMATICS FACULTY OF SCIENCE AND ARTS GAZI UNIVERSITY)
  • Published : 2008.01.31
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Abstract

In this paper, we give some fixed point theorems on fuzzy metric spaces with an implicit relation. Our results extend and generalize some fixed point theorems on complete fuzzy metric spaces by using a new technique.

Keywords

References

  1. R. Badard, Fixed point theorems for fuzzy numbers, Fuzzy Sets and Systems 13 (1984), 291-302 https://doi.org/10.1016/0165-0114(84)90063-0
  2. B. K. Bose and D. Sahani, Fuzzy mappings and fixed point theorems, Fuzzy Sets and Systems 21 (1987), 53-58 https://doi.org/10.1016/0165-0114(87)90152-7
  3. D. Butnariu, Fixed points for fuzzy mappings, Fuzzy Sets and Systems 7 (1982), 191-207 https://doi.org/10.1016/0165-0114(82)90049-5
  4. S. S. Chang, Fixed point theorems for fuzzy mappings, Fuzzy Sets and Systems 17 (1985), 181-187 https://doi.org/10.1016/0165-0114(85)90055-7
  5. S. S. Chang, Y. J. Cho, B. S. Lee, J. S. Jung, and S. M. Kang, Coincidence point and minimization theorems in fuzzy metric spaces, Fuzzy Sets and Systems 88 (1997), 119-128 https://doi.org/10.1016/S0165-0114(96)00060-7
  6. S. S. Chang, Y. J. Cho, B. E. Lee, and G. M. Lee, Fixed degree and fixed point theorems for fuzzy mappings, Fuzzy Sets and Systems 87 (1997), 325-334 https://doi.org/10.1016/0165-0114(95)00373-8
  7. Y. J. Cho, Fixed points in fuzzy metric spaces, J. Fuzzy Math. 5 (1997), 949-962
  8. Y. J. Cho, H. K. Pathak, S. M. Kang, and J. S. Jung, Common fixed points of compatible maps of type ($\beta$) on fuzzy metric spaces, Fuzzy Sets and Systems 93 (1998), 99-111 https://doi.org/10.1016/S0165-0114(96)00200-X
  9. J. X. Fang, On fixed point theorems in fuzzy metric spaces, Fuzzy Sets and Systems 46 (1992), 107-113 https://doi.org/10.1016/0165-0114(92)90271-5
  10. 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
  11. M. Grabiec, Fixed points in fuzzy metric spaces, Fuzzy Sets and Systems 27 (1988), 385-389 https://doi.org/10.1016/0165-0114(88)90064-4
  12. O. Hadzic, Fixed point theorems for multi-valued mappings in some classes of fuzzy metric spaces, Fuzzy Sets and Systems 29 (1989), 115-125 https://doi.org/10.1016/0165-0114(89)90140-1
  13. M. Imdad, S. Kumar, and M. S. Khan, Remarks on some fixed point theorems satisfying implicit relations, Rad. Math. 11 (2002), 135-143
  14. J. S. Jung, Y. J. Cho, and J. K. Kim, Minimization theorems for fixed point theorems in fuzzy metric spaces and applications, Fuzzy Sets and Systems 61 (1994), 199-207 https://doi.org/10.1016/0165-0114(94)90234-8
  15. J. S. Jung, Y. J. Cho, S. S. Chang, and S. M. Kang, Coincidence theorems for setvalued mappings and Ekland's variational principle in fuzzy metric spaces, Fuzzy Sets and Systems 79 (1996), 239-250 https://doi.org/10.1016/0165-0114(95)00084-4
  16. S. N. Mishra, S. N. Sharma, and S. L. Singh, Common fixed points of maps in fuzzy metric spaces, Internat. J. Math. Math. Sci. 17 (1994), 253-258 https://doi.org/10.1155/S0161171294000372
  17. V. Popa, A general coincidence theorem for compatible multivalued mappings satisfying an implicit relation, Demonsratio Math. 33 (2000), 159-164
  18. V. Popa, Some fixed point theorems for compatible mappings satisfying an implicit relation, Demonsratio Math. 32 (1999), 157-163
  19. V. Popa and D. Turkoglu, Some fixed point theorems for hybrid contractions satisfying an implicit relation, Stud. Cercet. Stint. Ser. Math. Univ. Bacau 8 (1998), 75-86
  20. B. Schweizer and A. Sklar, Statistical metric spaces, Pacific J. Math. 10 (1960), 313-334 https://doi.org/10.2140/pjm.1960.10.313
  21. S. Sharma, Common fixed point theorems in fuzzy metric spaces, Fuzzy Sets and Systems 127 (2002), 345-352 https://doi.org/10.1016/S0165-0114(01)00112-9
  22. S. Sharma and B. Desphande, Common fixed points of compatible maps of type ($\beta$) on fuzzy metric spaces, Demonsratio Math. 35 (2002), 165-174
  23. S. Sharma and B. Desphande, On compatible mappings satisfying an implicit relation in common fixed point consideration, Tamkang J. Math. 33 (2002), 245-252
  24. B. Singh and M. S. Chauhan, Common fixed points of compatible maps in fuzzy metric spaces, Fuzzy Sets and Systems 115 (2000), 471-475 https://doi.org/10.1016/S0165-0114(98)00099-2
  25. L. A. Zadeh, Fuzzy sets, Inform and Control 8 (1965), 338-353 https://doi.org/10.1016/S0019-9958(65)90241-X

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