Article
Full entry |
PDF
(0.2 MB)
Feedback
PDF
(0.2 MB)
Feedback
Keywords:
fuzzy metric space; common fixed points; $t$-norm; compatible maps of type $ (\beta ) $; compatible maps of type $ (\alpha ) $; weak compatible maps
fuzzy metric space; common fixed points; $t$-norm; compatible maps of type $ (\beta ) $; compatible maps of type $ (\alpha ) $; weak compatible maps
Summary:
The object of this paper is to establish a unique common fixed point theorem for six self-mappings satisfying a generalized contractive condition through compatibility of type $ ( \beta ) $ and weak compatibility in a fuzzy metric space. It significantly generalizes the result of Singh and Jain [The Journal of Fuzzy Mathematics $(2006)] $ and Sharma [Fuzzy Sets and Systems $(2002) ] $. An example has been constructed in support of our main result. All the results presented in this paper are new.
References:
[1] Cho, Y. J.: Fixed point in fuzzy metric space. J. Fuzzy Math. 5 (1997), 949-962.
[2] Cho, Y. J., Pathak, H. K., Kang, S. M., Jung, J. S.: Common fixed points of compatible maps of type $(\beta)$ on fuzzy metric spaces. Fuzzy Sets Syst. 93 (1998), 99-111. MR 1600404 | Zbl 0915.54004
[3] Geroge, A., Veeramani, P.: On some results in fuzzy metric spaces. Fuzzy Sets Syst. 64 (1994), 395-399. MR 1289545
[4] Grabiec, M.: Fixed points in fuzzy metric spaces. Fuzzy Sets Syst. 27 (1988), 385-389. MR 0956385 | Zbl 0664.54032
[5] Jungck, G.: Compatible mappings and common fixed point. Int. J. Math. Math. Sci. 9 (1986), 771-779. DOI 10.1155/S0161171286000935 | MR 0870534
[6] Jungck, G., Rhoades, B. E.: Fixed point for set valued functions with out continuity. Indian J. Pure Appl. Math. 29 (1998), 227-238. MR 1617919
[7] Kramosil, I., Michalek, J.: Fuzzy metric and statistical metric spaces. Kybernetica 11 (1975), 326-334. MR 0410633
[8] Mishra, S. N., Singh, S. L.: Common fixed points of maps in fuzzy metric spaces. Int. J. Math. Math. Sci. 17 (1994), 253-258. DOI 10.1155/S0161171294000372 | MR 1261071
[9] Sessa, S.: On a weak commutative condition in fixed point consideration. Publ. Inst. Math. (Beograd) 32 (1982), 146-153. MR 0710984
[10] Sharma, S.: Common fixed point theorem in fuzzy metric space. Fuzzy Sets Syst. 127 (2002), 345-352. DOI 10.1016/S0165-0114(01)00112-9 | MR 1899067
[11] Singh, B., Chouhan, M. S.: Common fixed point theorems in fuzzy metric space. Fuzzy Sets Syst. 115 (2000), 471-475.
[12] Singh, B., Jain, S.: Fixed point theorem for six self maps in fuzzy metric space. J. Fuzzy Math. 14 (2006), 231-243. MR 2211701
[13] Vasuki, R.: Common fixed points for $R$-weakly commuting maps in fuzzy metric space. Indian J. Pure Appl. Math. (1999), 419-423. MR 1695690
[14] Zadeh, L. A.: Fuzzy Sets. Inf. Control. 89 (1965), 338-353. DOI 10.1016/S0019-9958(65)90241-X | MR 0219427 | Zbl 0139.24606
Search
Partner of
