Title:
|
Fixed points theorems of non-expanding fuzzy multifunctions (English) |
Author:
|
Stouti, Abdelkader |
Language:
|
English |
Journal:
|
Archivum Mathematicum |
ISSN:
|
0044-8753 (print) |
ISSN:
|
1212-5059 (online) |
Volume:
|
41 |
Issue:
|
1 |
Year:
|
2005 |
Pages:
|
117-122 |
Summary lang:
|
English |
. |
Category:
|
math |
. |
Summary:
|
We prove the existence of a fixed point of non-expanding fuzzy multifunctions in $\alpha $-fuzzy preordered sets. Furthermore, we establish the existence of least and minimal fixed points of non-expanding fuzzy multifunctions in $\alpha $-fuzzy ordered sets. (English) |
Keyword:
|
fuzzy set |
Keyword:
|
$\alpha $-fuzzy preorder relation |
Keyword:
|
$\alpha $-fuzzy order relation |
Keyword:
|
non-expanding fuzzy multifunction |
Keyword:
|
fixed point |
MSC:
|
03E72 |
MSC:
|
06A99 |
MSC:
|
06D72 |
MSC:
|
47H04 |
MSC:
|
47H10 |
MSC:
|
54H25 |
idZBL:
|
Zbl 1108.03053 |
idMR:
|
MR2142147 |
. |
Date available:
|
2008-06-06T22:45:20Z |
Last updated:
|
2012-05-10 |
Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107939 |
. |
Reference:
|
[1] Beg I., Islam M.: Fuzzy order linear spaces.J. Fuzzy Math. 3 (3) (1995), 659–670. MR 1353830 |
Reference:
|
[2] Beg I.: Fixed points of fuzzy multivalued mappings with values in fuzzy ordered sets.J. Fuzzy Math. 6 (1) (1998), 127–131. Zbl 0909.47055, MR 1609883 |
Reference:
|
[3] Beg I.: 0n fuzzy Zorn’s lemma.Fuzzy Sets and Systems 101 (1999), 181–183. MR 1658920 |
Reference:
|
[4] Beg I.: Fixed points of expansive mappings on fuzzy preordered sets.J. Fuzzy Math., 7(2)(1999), 397-400. Zbl 0941.54037, MR 1697747 |
Reference:
|
[5] Beg I.: Fixed points of fuzzy monotone maps.Arch. Math. (Brno) 35 (1999), 141–144. Zbl 1047.03044, MR 1711740 |
Reference:
|
[6] Bose B. K., Sahani D.: Fuzzy mappings and fixed point theorems.Fuzzy Sets and Systems 21 (1987), 53–58. Zbl 0609.54032, MR 0868355 |
Reference:
|
[7] Billot A.: Economic theory of fuzzy equilibria.Lecture Notes in Econom. and Math. Systems 373 Springer-Verlag, Berlin 1992. Zbl 0758.90008, MR 1227785 |
Reference:
|
[8] Fang J. X.: On fixed point theorems in fuzzy metric spaces.Fuzzy Sets and Systems 46 (1992), 107–113. Zbl 0766.54045, MR 1153595 |
Reference:
|
[9] Hadzic O.: Fixed point theorems for multivalued mapping in some classes of fuzzy metric spaces.Fuzzy Sets and Systems 29 (1989), 115–125. MR 0976292 |
Reference:
|
[10] Heilpern S.: Fuzzy mappings and fixed point theorems.J. Math. Anal. Appl. 83 (1981), 566–569. MR 0641351 |
Reference:
|
[11] Kaleva O.: A note on fixed points for fuzzy mappings.Fuzzy Sets and Systems 15 (1985), 99–100. Zbl 0564.47028, MR 0785284 |
Reference:
|
[12] Negoita C. V., Ralescu D. A.: Applications of fuzzy sets to systems analysis.Fuzzy Sets and Systems 1 (1978), 155–167. |
Reference:
|
[13] Stouti A.: Fixed point theory for fuzzy monotone multifunctions.J. Fuzzy Math. 11 (2) (2003), 455–466. Zbl 1053.54014, MR 1982177 |
Reference:
|
[14] Stouti A.: Fixed points of fuzzy monotone multifunctions.Arch. Math. (Brno) 39 (2003), 209–212. Zbl 1108.03312, MR 2010722 |
Reference:
|
[15] Stouti A.: A fuzzy version of Tarski’s fixpoint Theorem.Arch. Math. (Brno) 40 (2004), 273–279. Zbl 1108.06008, MR 2107022 |
Reference:
|
[16] Stouti A.: Fixed points of expanding fuzzy multifunctions.J. Fuzzy Math. 12(4) (2004), 1542–1546. Zbl 1079.54022, MR 2125751 |
Reference:
|
[17] Venugopalan P.: Fuzzy ordered sets.Fuzzy Sets and Systems 46 (1992), 221–226. Zbl 0765.06008, MR 1167316 |
Reference:
|
[18] Zadeh L. A.: Fuzzy sets.Information and Control 8 (1965), 338–353. Zbl 0139.24606, MR 0219427 |
Reference:
|
[19] Zadeh L. A.: Similarity and fuzzy ordering.Information Sciences 3 (1971), 177–200. MR 0297650 |
. |