RELATED FIXED POINT THEOREM ON TWO INTUITIONISTIC FUZZY METRIC SPACES

  • Deshpande, Bhavana (DEPARTMENT OF MATHEMATICS, GOVA. ARTS AND SCIENCE P.G. COLLEGE) ;
  • Pathak, Rohit (DEPARTMENT OF APPLIED MATHEMATICS, INSTITUTE OF ENGINEERING AND TECHNOLOGY)
  • 발행 : 2009.11.30

초록

We prove a related fixed point theorem for two pairs of mappings on two intuitionistic fuzzy metric spaces. Our result is maiden in this line.

키워드

참고문헌

  1. K. Atanassov: Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20 (1986), 87-96. https://doi.org/10.1016/S0165-0114(86)80034-3
  2. C. Alaca, D. Turkoglu & C. Yildiz: Fixed points in intuitionistic fuzzy metric spaces. Chaos Solitons & Fractals 29 (2006), 1073-1078. https://doi.org/10.1016/j.chaos.2005.08.066
  3. S. Banach: Theorie les Operations Linearies. Manograie Mathematyezne, Warsaw, Poland, 1932.
  4. Y. J . Cho, S.M. Kang & S.S. Kim: Fixed points in two metric spaces. Novi. Sad. J. Math. 29 (1999), no. 1, 47-53.
  5. D. Dubois & H. Prade: Fuzzy sets: theory and applications to policy analysis and formations systems. New York, Plenum Press, 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. El Naschie MS.: On the uncertainity of cantorian geometry and two-slit experiments. Chaos Solitons & Fractals 9 (1998), no. 5, 17-29.
  8. El Naschie MS: On the verification of heterotic strings theory and ${\varrho}^({\infty})$ theory. Chaos Solitons & Fractals 11 (2000), 2397-2408. https://doi.org/10.1016/S0960-0779(00)00108-9
  9. El Naschie MS: The two slit experiments as the foundation of E- infinity of high energy physics. Chaos Solitons & Fractals 25 (2005), 509-514. https://doi.org/10.1016/j.chaos.2005.02.016
  10. El Naschie MS: tHooft ultimate building blocks and space-time an infinite dimensional set of transfinite discrete points. Chaos Solitons & Fractals 25 (2005), 521-524. https://doi.org/10.1016/j.chaos.2005.01.022
  11. B. Fisher: Fixed point on two metric spaces. Glasnik Math. 16 (1981), no. 36, 333-337.
  12. B. Fisher: Related fixed points on two metric spaces. Math. Seminar Notes Kobe Univ. 10 (1982), 17-26.
  13. B. Fisher & P.P. Murthy: Related fixed point theorems for two pairs of mappings on two metric spaces. Kyungpook Math. J. 37 (1997), 343-347.
  14. A. George & P. Veeramani: On some results in fuzzy metric spaces. Fuzzy Sets Syst. 64 (1994), 395-399. https://doi.org/10.1016/0165-0114(94)90162-7
  15. M. Grabiec: Fixed points in fuzzy metric spaces. Fuzzy Sets Syst. 27 (1988), 385-389. https://doi.org/10.1016/0165-0114(88)90064-4
  16. V. Gregory, S. Romaguera & P. Veeramani: A note on intuitionistic fuzzy metric spaces. Chaos Solitons & Fractals 28 (2006), 902-905. https://doi.org/10.1016/j.chaos.2005.08.113
  17. E.P. Klement: Operations on fuzzy sets an axiomatic approach. Inform. Sci. 27 (1984), 221-232. https://doi.org/10.1016/0020-0255(82)90026-3
  18. E.P. Klement, R. Mesiar & E. Pap: Triangular norma. Trends in logic. Dordrecht, Kluwer Academic Publishers 8, 2000.
  19. O. Kramosil & J. Michalek: Fuzzy metric and statistical spaces. Kybernetica 11 (1975), 326-334.
  20. R. Lowen: Fuzzy sets theory. Dordrecht, Kluwer Academic Publishers, 1996.
  21. K. Menger: Statistical metric. Proc. Nat. Acad. Sci. 28 (1942), 535-537. https://doi.org/10.1073/pnas.28.12.535
  22. S.N. Mishra , N. Sharma & S.L.Singh: Common fixed points of maps on fuzzy metric spaces. Int. J. Math. Sci. 17 (1994), 253-288. https://doi.org/10.1155/S0161171294000372
  23. N.P. Nung: A fixed point theorem in three metric spaces. Math. Sem. Notes Kobe Univ. 11 (1983).
  24. J.H. Park: Intuitionistic fuzzy metric spaces. Chaos Solitons & Fractals 22 (2004), 1039-1046. https://doi.org/10.1016/j.chaos.2004.02.051
  25. R. Saadati & J.H. Park: On the intuitionistic topological spaces. Chaos Solitons & Fractals 27 (2006), 331-344. https://doi.org/10.1016/j.chaos.2005.03.019
  26. B. Schweizer & A. Sklar: Statistical metric spaces. Pacific J. Math. 10 (1960), 314-334.
  27. S. Sharma & B. Deshpande: Common fixed point theorems for finite number of mappings without continuity and compatibility on intuitionistic fuzzy metric spaces. Chaos Solitons & Fractals 40 (2009), 2242-2256. https://doi.org/10.1016/j.chaos.2007.10.011
  28. S. Sharma, B. Deshpande & D. Thakur: Related fixed point theorem for four mappings on two fuzzy metric spaces. Int. J. Pure and Appl. Math. 41 (2007), no. 2, 241-250.
  29. R.R. Yager: On a class of weak triangular norm operators. Inform. Sci. 96 (1997), no. 1-2, 47-78. https://doi.org/10.1016/S0020-0255(96)00140-5