Title: Common Fixed Point Theorems for Four Fuzzy Mappings
Author(s): Animesh Gupta, Neelesh Pandey
Pages: 97-112
Cite as:
Animesh Gupta, Neelesh Pandey, Common Fixed Point Theorems for Four Fuzzy Mappings, Int. J. Anal. Appl., 6 (1) (2014), 97-112.

Abstract


In this paper, we obtain some common fixed point theorems for four fuzzy mappings in complete ordered metric linear spaces. These mappings are assumed to satisfy certain contractive inequality involving functions which are generalizations of altering distance functions. We also note that this fuzzy fixed point result is derivable from a multi-valued fixed point result.

Full Text: PDF

 

References


  1. M. Abbas, N. Talat, S. Radenovic, Common fixed points of four maps in partially ordered metric spaces, Appl. Math. Lett, 24(2011), 1520-1526.

  2. H.M. Abu-Donia, Common fixed points theorems for fuzzy mappings in metric spaces under ψ- contraction condition, Chaos, Solitons & Fractals 34 (2007), 538–543.

  3. S.C. Arora, V. Sharma, Fixed points for fuzzy mappings, Fuzzy Sets and Systems 110 (2000), 127–130.

  4. A. Azam, M. Arshad, A note on fixed point theorems for fuzzy mappings by P.Vijayaraju and M. Marudai, Fuzzy Sets and Systems 161 (2010), 1145–1149.

  5. A. Azam,I. Beg ,Common fixed points of fuzzy maps, Math. Comp. Modelling 49 (2009), 1331-1336.

  6. B. S. Choudhury and A. Upadhyay, On unique common fixed point for a sequence of multivalued mappings on metric spaces, Bulletin of Pure and Applied Science, 19E(2000), 529-533.

  7. B. S. Choudhury and P. N. Dutta, A unified fixed point result in metric spaces involving a two variable function, FILOMAT, 14(2000), 43-48.

  8. B. S. Choudhury and P. N. Dutta, A unified approach to fixed points of self-mappings in metric spaces, (Preprint).

  9. B.S. Choudhury, A common unique fixed point result in metric spaces involving generalized altering distance, Math. Comm., 10(2005), 105–110.

  10. V.D. Estruch and A. Vidal, A note on fixed fuzzy points for fuzzy mappings, Rend. Istit. Univ. Trieste, 32(2011),39–45.

  11. S. Heilpern, Fuzzy mappings and fixed point theorems, J.Math. Anal. Appl., 83(1981), 566– 569.

  12. G. Jungck, Compatible mappings and common fixed points, Internat. J. Math. Math. Sci. 9(1986), 771–779.

  13. M. S. Khan, M. Swaleh and S. Sessa, Fixed point theorem by altering distances between the points, Bull. Austral. Math. Soc., 30(1984), 1-9.

  14. B.S. Lee, G.M. Lee, S.J. Cho, D.S. Kim, a common fixed point theorem for a pair of fuzzy mappings, Fuzzy Sets and Systems, 98 (1998), 133-136.

  15. B.S. Lee, S.J. Cho, Common fixed point theorems for a sequence of fuzzy mappings, Internat. J. Math & Math Sciences, 17, No. 3 (1994), 423-428.

  16. S.B. Nadler Jr., Multivalued contraction mappings, Pacific Journal of Math., 30 (1969), 475-487.

  17. C. V. Negoita, D. Ralescu, Representation theorem for fuzzy concepts, Kybernets, 4 (1975), 169-174.

  18. K.P.R. Rao , G. Ravi Babu , D. Vasu Babu, Common fixed point theorem through generalized altering distance functions, Math. Comm. 13(2008), 64-73.

  19. A.C.M. Ran, M.C.B. Reurings, A fixed point theorem in partially ordered sets and some application to matrix equations, Proc. Amer. Math. Soc., 132 (2004), 1435-1443.

  20. K. P. R. Sastry and G. V. R. Babu, Fixed point theorems in metric spaces by altering distances, Bull. Cal. Math. Soc., 90(1998), 175-182.

  21. K. P. R. Sastry, S. V. R. Naidu, G. V. R. Babu and G. A. Naidu, Generalisation of common fixed point theorems for weakly commuting maps by altering distances, Tamkang J. Math., 31(2000), 243-250.

  22. S. Sessa, On a weak commutativity condition of mappings in fixed point considerations, Publ. Inst. Math. (Beograd) 32 (1982), 149-153.

  23. L.A. Zadeh, Fuzzy sets, Informatics and Control, 8(1965), 103–112.