DOI QR코드

DOI QR Code

Related Fixed Point Theorem for Six Mappings on Three Fuzzy Metric Spaces

  • Sharma, Sushil (Department of Mathematics, Madhav Science College, Vikram University) ;
  • Tilwankar, Prashant (Department of Mathematics, Shri Vaishnav Institute of Management, Devi Ahilya University)
  • 투고 : 2010.01.13
  • 심사 : 2011.03.07
  • 발행 : 2011.11.23

초록

Related fixed point theorems on two or three metric spaces have been prove in different ways. However, so for the related fixed point theorem on fuzzy metric space have not been proved. Sharma, Deshpande and Thakur were the first who have establishe related fixed point theorem for four mappings on two complete fuzzy metric spaces. Their work was maiden in this line. In this paper we obtain a related fixed point theorem for six mappings on three complete fuzzy metric spaces. Of course this is a new result on this line.

키워드

참고문헌

  1. Y. J. Cho, Fixed points in fuzzy metric spaces, Journal of Fuzzy Mathematics, 5(4)(1997), 949-962.
  2. Y. J. Cho, S. M. Kang and S. S. Kim, Fixed points in two metric spaces, Novi Sad J. Math., 29(1)(1999), 47-53.
  3. Z. K. Deng, Fuzzy pseudo metric spaces, J. Math. Anal. Appl., 86(1982), 74-75. https://doi.org/10.1016/0022-247X(82)90255-4
  4. M. A. Erceg, Metric spaces in fuzzy set theory, J. Math. Anal. Appl., 69(1979), 205-230. https://doi.org/10.1016/0022-247X(79)90189-6
  5. B. Fisher, Fixed points on two metric spaces, Glasnik Mate, 16(36)(1981), 333-337.
  6. B. Fisher, Related fixed points on two metric spaces, Math. Seminar Notes, Kobe Univ., 10(1982), 17-26.
  7. B. Fisher and P. P. Murthy, Related fixed point theorems for two pairs of mappings on two metric spaces, Kyungpook Math. J., 37(1997), 343-347.
  8. 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
  9. M. Grabiec, Fixed point in fuzzy metric space, Fuzzy Sets and Systems, 27(1988), 385-389. https://doi.org/10.1016/0165-0114(88)90064-4
  10. R. K. Jain, H. K. Sahu and B. Fisher, Related fixed point theorems for three metric spaces, Novi Sad J. Math., 26(1)( 1996), 11-17.
  11. R. K. Jain, A. K. Shrivastava and B. Fisher, Fixed points on three complete metric spaces, Novi Sad J. Math., 27(1)(1997), 27-35.
  12. O. Kaleva and S. Seikkala, On fuzzy metric spaces, Fuzzy Sets and Systems, 12(1984), 215-229. https://doi.org/10.1016/0165-0114(84)90069-1
  13. O. Kramosil and J. Michalek, Fuzzy metric and statistical metric spaces, Kybernetica, 11(1975), 336-344.
  14. S. N. Mishra, N. Sharma and S. L. Singh, Common fixed points of maps on fuzzy metric spaces, Internat. J. Math. Sci., 17(1994), 253-258. https://doi.org/10.1155/S0161171294000372
  15. N. P. Nung, A fixed point theorem in three metric spaces, Math. Seminar Notes, Kobe Univ., 11(1983), 77-79.
  16. V. Popa, Fixed points on two complete metric spaces, Review of Research, Faculty of Sci. Math. Series Univ. of Novi Sad, 21(1)(1991), 83-93.
  17. B. Schweizer and A. Sklar, Statistical spaces, Pacific J. Math., 10(1960), 313-334. https://doi.org/10.2140/pjm.1960.10.313
  18. Sushil Sharma, Bhavna Deshpande and Deepti Thakur, Related fixed point theorem for four mappings on two fuzzy metric spaces, Internet. J. Pure and Applied Mathematics, 41(2)(2007), 241-250.
  19. L. A. Zadeh, Fuzzy Sets, Information and control, 8(1965), 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X