| Title:
|
On best approximation in fuzzy metric spaces (English) |
| Author:
|
Abbasi, Naser |
| Author:
|
Mottaghi Golshan, Hamid |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 (print) |
| ISSN:
|
1805-949X (online) |
| Volume:
|
51 |
| Issue:
|
2 |
| Year:
|
2015 |
| Pages:
|
374-386 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we introduce the notation of t-best approximatively compact sets, t-best approximation points, t-proximinal sets, t-boundedly compact sets and t-best proximity pair in fuzzy metric spaces. The results derived in this paper are more general than the corresponding results of metric spaces, fuzzy metric spaces, fuzzy normed spaces and probabilistic metric spaces. (English) |
| Keyword:
|
best approximation |
| Keyword:
|
topology |
| Keyword:
|
fuzzy metric spaces |
| MSC:
|
41A50 |
| MSC:
|
54A40 |
| idZBL:
|
Zbl 06487085 |
| idMR:
|
MR3350568 |
| DOI:
|
10.14736/kyb-2015-2-0374 |
| . |
| Date available:
|
2015-06-19T15:28:56Z |
| Last updated:
|
2016-01-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144304 |
| . |
| Reference:
|
[1] Beer, G., Pai, D.: Proximal maps, prox maps and coincidence points..Numer. Funct. Anal. Optim. 11 (1990), 5-6, 429-448. Zbl 0726.41035, MR 1079285, 10.1080/01630569008816382 |
| Reference:
|
[2] Chang, S. S., Cho, Y. J., Kang, S. M.: Nonlinear Operator Theory in Probabilistic Metric Spaces..Nova Science Publishers Inc, New York 2001. Zbl 1080.47054, MR 2018691 |
| Reference:
|
[3] Eldred, A. A., Veeramani, P.: Existence and convergence of best proximity points..J. Math. Anal. Appl. 323 (2006), 2, 1001-1006. Zbl 1105.54021, MR 2260159, 10.1016/j.jmaa.2005.10.081 |
| Reference:
|
[4] George, A., Veeramani, P.: On some results in fuzzy metric spaces..Fuzzy Sets and Systems 64 (1994), 3, 395-399. Zbl 0843.54014, MR 1289545, 10.1016/0165-0114(94)90162-7 |
| Reference:
|
[5] George, A., Veeramani, P.: On some results of analysis for fuzzy metric spaces..Fuzzy Sets and Systems 90 (1997), 3, 365-368. Zbl 0917.54010, MR 1477836, 10.1016/s0165-0114(96)00207-2 |
| Reference:
|
[6] Grabiec, M.: Fixed points in fuzzy metric spaces..Fuzzy Sets and Systems 27 (1998), 3, 385-389. Zbl 0664.54032, MR 0956385, 10.1016/0165-0114(88)90064-4 |
| Reference:
|
[7] Gregori, V., Romaguera, S.: Characterizing completable fuzzy metric spaces..Fuzzy Sets and Systems 144 (2004), 3, 411-420. Zbl 1057.54010, MR 2061403, 10.1016/s0165-0114(03)00161-1 |
| Reference:
|
[8] Gregori, V., Romaguera, S.: Some properties of fuzzy metric spaces..Fuzzy Sets and Systems 115 (2000), 3, 485-489. Zbl 0985.54007, MR 1781550, 10.1016/s0165-0114(98)00281-4 |
| Reference:
|
[9] Hadžić, O., Pap, E.: Fixed Point Theory in Probabilistic Metric Spaces..Kluwer Academic Publishers, Dordrecht 2001. Zbl 1265.54127, MR 1896451, 10.1007/978-94-017-1560-7 |
| Reference:
|
[10] Kainen, P. C.: Replacing points by compacta in neural network approximation..J. Franklin Inst. 341 (2004), 4, 391-399. Zbl 1075.54013, MR 2071890, 10.1016/j.jfranklin.2004.03.001 |
| Reference:
|
[11] Kirk, W. A., Srinivasan, P. S., Veeramani, P.: Fixed points for mappings satisfying cyclical contractive conditions..Fixed Point Theory 4 (2003), 1, 79-89. Zbl 1052.54032, MR 2031823 |
| Reference:
|
[12] Kramosil, I., Michálek, J.: Fuzzy metrics and statistical metric spaces..Kybernetika 11 (1975), 5, 336-344. Zbl 0319.54002, MR 0410633 |
| Reference:
|
[13] Menger, K.: Statistical metrics..Proc. Nat. Acad. Sci. U. S., A. 28 (1942), 535-537. Zbl 0063.03886, MR 0007576, 10.1073/pnas.28.12.535 |
| Reference:
|
[14] Rodríguez-López, J., Romaguera, S.: The Hausdorff fuzzy metric on compact sets..Fuzzy Sets and Systems 147 (2004), 2, 273-283. Zbl 1069.54009, MR 2089291, 10.1016/j.fss.2003.09.007 |
| Reference:
|
[15] Romaguera, S., Sanchis, M.: On fuzzy metric groups..Fuzzy Sets and Systems 124 (2001), 1, 109-115. Zbl 0994.54007, MR 1859783, 10.1016/s0165-0114(00)00085-3 |
| Reference:
|
[16] Sahney, B. E., Singh, S. P.: On best simultaneous approximation..In: Approximation Theory III (E. W. Cheney, ed.), 1980, pp. 783-789. Zbl 0489.41033, MR 0602802 |
| Reference:
|
[17] Schweizer, B., Sklar, A.: Statistical metric spaces..Pacific J. Math. 10 (1960), 314-334. Zbl 0136.39301, MR 0115153, 10.2140/pjm.1960.10.313 |
| Reference:
|
[18] Shams, M., Vaezpour, S. M.: Best approximation on probabilistic normed spaces..Chaos Solitons Fractals 41 (2009), 4, 1661-1667. Zbl 1200.46072, MR 2537771, 10.1016/j.chaos.2008.07.009 |
| Reference:
|
[19] Singer, I.: Best Approximation in Normed Linear Spaces by Elements of Linear Subspaces..Springer-Verlag 1970. Zbl 0197.38601, MR 0270044, 10.1007/978-3-662-41583-2 |
| Reference:
|
[20] Vaezpour, S. M., Karimi, F.: t-best approximation in fuzzy normed spaces..Iran. J. Fuzzy Syst. 5 (2008), 2, 93-99. Zbl 1171.46051, MR 2432015 |
| Reference:
|
[21] Veeramani, P.: Best approximation in fuzzy metric spaces..J. Fuzzy Math. 9 (2001), 1, 75-80. Zbl 0986.54006, MR 1822315 |
| Reference:
|
[22] Xu, X.: A result on best proximity pair of two sets..J. Approx. Theory 54 (1988), 3, 322-325. Zbl 0653.41030, MR 0960054, 10.1016/0021-9045(88)90008-1 |
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