| Title:
|
Urysohn’s lemma, gluing lemma and contraction$^*$ mapping theorem for fuzzy metric spaces (English) |
| Author:
|
Roja, E. |
| Author:
|
Uma, M. K. |
| Author:
|
Balasubramanian, G. |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
133 |
| Issue:
|
2 |
| Year:
|
2008 |
| Pages:
|
179-185 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper the concept of a fuzzy contraction$^*$ mapping on a fuzzy metric space is introduced and it is proved that every fuzzy contraction$^*$ mapping on a complete fuzzy metric space has a unique fixed point. (English) |
| Keyword:
|
fuzzy contraction mapping |
| Keyword:
|
fuzzy continuous mapping |
| MSC:
|
03E72 |
| MSC:
|
54A40 |
| MSC:
|
54E35 |
| MSC:
|
54H25 |
| idZBL:
|
Zbl 1199.54243 |
| idMR:
|
MR2428313 |
| DOI:
|
10.21136/MB.2008.134052 |
| . |
| Date available:
|
2009-09-24T22:36:01Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134052 |
| . |
| Reference:
|
[1] M. A. Erceg: Metric spaces in fuzzy set theory.J. Math. Anal. Appl. 69 (1979), 205–230. Zbl 0409.54007, MR 0535292, 10.1016/0022-247X(79)90189-6 |
| Reference:
|
[2] A. George, P. Veeramani: On some results in fuzzy metric spaces.Fuzzy Sets Syst. 64 (1994), 395–399. MR 1289545 |
| Reference:
|
[3] A. George, P. Veeramani: Some theorems in fuzzy metric spaces.J. Fuzzy Math. 3 (1995), 933–940. MR 1367026 |
| Reference:
|
[4] A. George, P. Veeramani: On some results of analysis for fuzzy metric spaces.Fuzzy Sets Syst. 90 (1997), 365–368. MR 1477836 |
| Reference:
|
[5] O. Kaleva, S. Seikkala: On fuzzy metric spaces.Fuzzy Sets Syst. 12 (1984), 215–229. MR 0740095 |
| Reference:
|
[6] G. Rajendran, G. Balasubramanian: Fuzzy contraction mapping theorem for fuzzy metric spaces.Bull. Calcutta Math. Soc. 94 (2002), 453–458. MR 1947762 |
| Reference:
|
[7] L. A. Zadeh: Fuzzy sets.Inform and Control 8 (1965), 338–353. Zbl 0139.24606, MR 0219427, 10.1016/S0019-9958(65)90241-X |
| Reference:
|
[8] Zi-Ke, Deng: Fuzzy pseudo metric spaces.J. Math. Anal. Appl. 86 (1982), 74–95. 10.1016/0022-247X(82)90255-4 |
| . |
