| Title:
|
Compatible mappings of type $(\beta)$ and weak compatibility in fuzzy metric spaces (English) |
| Author:
|
Jain, Shobha |
| Author:
|
Jain, Shishir |
| Author:
|
Jain, Lal Bahadur |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
134 |
| Issue:
|
2 |
| Year:
|
2009 |
| Pages:
|
151-164 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| 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. (English) |
| Keyword:
|
fuzzy metric space |
| Keyword:
|
common fixed points |
| Keyword:
|
$t$-norm |
| Keyword:
|
compatible maps of type $ (\beta ) $ |
| Keyword:
|
compatible maps of type $ (\alpha ) $ |
| Keyword:
|
weak compatible maps |
| MSC:
|
47H10 |
| MSC:
|
54H25 |
| idZBL:
|
Zbl 1212.54117 |
| idMR:
|
MR2535143 |
| DOI:
|
10.21136/MB.2009.140650 |
| . |
| Date available:
|
2010-07-20T17:55:11Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140650 |
| . |
| Reference:
|
[1] Cho, Y. J.: Fixed point in fuzzy metric space.J. Fuzzy Math. 5 (1997), 949-962. |
| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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[5] Jungck, G.: Compatible mappings and common fixed point.Int. J. Math. Math. Sci. 9 (1986), 771-779. MR 0870534, 10.1155/S0161171286000935 |
| Reference:
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| Reference:
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| Reference:
|
[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. MR 1261071, 10.1155/S0161171294000372 |
| Reference:
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[9] Sessa, S.: On a weak commutative condition in fixed point consideration.Publ. Inst. Math. (Beograd) 32 (1982), 146-153. MR 0710984 |
| Reference:
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[10] Sharma, S.: Common fixed point theorem in fuzzy metric space.Fuzzy Sets Syst. 127 (2002), 345-352. MR 1899067, 10.1016/S0165-0114(01)00112-9 |
| Reference:
|
[11] Singh, B., Chouhan, M. S.: Common fixed point theorems in fuzzy metric space.Fuzzy Sets Syst. 115 (2000), 471-475. |
| Reference:
|
[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 |
| Reference:
|
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| Reference:
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| . |
