| Title:
|
Countable extension of triangular norms and their applications to the fixed point theory in probabilistic metric spaces (English) |
| Author:
|
Hadžić, Olga |
| Author:
|
Pap, Endre |
| Author:
|
Budinčević, Mirko |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
38 |
| Issue:
|
3 |
| Year:
|
2002 |
| Pages:
|
[363]-382 |
| . |
| Category:
|
math |
| . |
| Keyword:
|
probabilistic metric space |
| Keyword:
|
triangular norm |
| Keyword:
|
Menger space |
| Keyword:
|
fixed point theorem |
| MSC:
|
47H10 |
| MSC:
|
47H40 |
| MSC:
|
47S50 |
| MSC:
|
54E70 |
| MSC:
|
54H25 |
| MSC:
|
60H25 |
| idZBL:
|
Zbl 1265.54127 |
| idMR:
|
MR1944316 |
| . |
| Date available:
|
2009-09-24T19:46:49Z |
| Last updated:
|
2015-03-25 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/135470 |
| . |
| Reference:
|
[1] J. Aczel: Lectures on Functional Equations and their Applications.Academic Press, New York 1969. MR 0208210 |
| Reference:
|
[2] O. Hadžič, E. Pap: On some classes of t-norms important in the fixed point theory.Bull. Acad. Serbe Sci. Art. Sci. Math. 25 (2000), 15-28. MR 1842812 |
| Reference:
|
[3] O. Hadžič, E. Pap: A fixed point theorem for multivalued mappings in probabilistic metric spaces and an application in fuzzy metric spaces.Fuzzy Sets and Systems 127 (2002), 333-344. MR 1899066 |
| Reference:
|
[4] O. Hadžič, E. Pap: Fixed Point Theory in Probabilistic Metric Spaces.Kluwer Academic Publishers, Dordrecht 2001. MR 1896451 |
| Reference:
|
[5] T. L. Hicks: Fixed point theory in probabilistic metric spaces.Univ. u Novom Sadu, Zb. Rad. Prirod.-Mat. Fak. Ser. Mat. 13 (1983), 63-72. Zbl 0574.54044, MR 0786431 |
| Reference:
|
[6] O. Kaleva, S. Seikalla: On fuzzy metric spaces.Fuzzy Sets and Systems 12 (1984), 215-229. MR 0740095, 10.1016/0165-0114(84)90069-1 |
| Reference:
|
[7] E. P. Klement R. Mesiar, and E. Pap: Triangular Norms.(Trends in Logic 8.) Kluwer Academic Publishers, Dordrecht 2000. MR 1790096 |
| Reference:
|
[8] E. P. Klement R. Mesiar, and E. Pap: Uniform approximation of associative copulas by strict and non-strict copulas.Illinois J. Math. J. 5 (2001), 4, 1393-1400. MR 1895466 |
| Reference:
|
[9] K. Menger: Statistical metric.Proc Nat. Acad. Sci. U.S.A. 28 (1942), 535-537. MR 0007576, 10.1073/pnas.28.12.535 |
| Reference:
|
[10] R. Mesiar, H. Thiele: On $T$-quantifiers and $S$-quantifiers: Discovering the World with Fuzzy Logic.(V. Novak and I. Perfilieva, eds., Studies in Fuzziness and Soft Computing vol. 57), Physica-Verlag, Heidelberg 2000, pp. 310-326. MR 1858106 |
| Reference:
|
[11] E. Pap: Null-Additive Set Functions.Kluwer Academic Publishers, Dordrecht and Ister Science, Bratislava 1995. Zbl 0968.28010, MR 1368630 |
| Reference:
|
[12] E. Pap O. Hadžič, and R. Mesiar: A fixed point theorem in probabilistic metric spaces and applications in fuzzy set theory.J. Math. Anal. Appl. 202 (1996), 433-449. MR 1406239, 10.1006/jmaa.1996.0325 |
| Reference:
|
[13] V. Radu: Lectures on probabilistic analysis. Surveys.(Lectures Notes and Monographs Series on Probability, Statistics & Applied Mathematics 2), Universitatea de Vest din Timisoara 1994. |
| Reference:
|
[14] B. Schweizer, A. Sklar: Probabilistic Metric Spaces.Elsevier North-Holland, New York 1983. Zbl 0546.60010, MR 0790314 |
| Reference:
|
[15] V. M. Sehgal, A. T. Bharucha-Reid: Fixed points of contraction mappings on probabilistic metric spaces.Math. Systems Theory 6 (1972), 97-102. Zbl 0244.60004, MR 0310858, 10.1007/BF01706080 |
| Reference:
|
[16] R. M. Tardiff: Contraction maps on probabilistic metric spaces.J. Math. Anal. Appl. 165 (1992), 517-523. Zbl 0773.54033, MR 1155736, 10.1016/0022-247X(92)90055-I |
| Reference:
|
[17] S. Weber: $\bot$-decomposable measures and integrals for Archimedean t-conorm $\bot$.J. Math. Anal. Appl. 101 (1984), 114-138. MR 0746230, 10.1016/0022-247X(84)90061-1 |
| . |
