On best approximation in fuzzy metric spaces

Naser Abbasi; Hamid Mottaghi Golshan

Kybernetika (2015)

  • Volume: 51, Issue: 2, page 374-386
  • ISSN: 0023-5954

Abstract

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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.

How to cite

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Abbasi, Naser, and Mottaghi Golshan, Hamid. "On best approximation in fuzzy metric spaces." Kybernetika 51.2 (2015): 374-386. <http://eudml.org/doc/270139>.

@article{Abbasi2015,
abstract = {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.},
author = {Abbasi, Naser, Mottaghi Golshan, Hamid},
journal = {Kybernetika},
keywords = {best approximation; topology; fuzzy metric spaces; best approximation; topology; fuzzy metric spaces},
language = {eng},
number = {2},
pages = {374-386},
publisher = {Institute of Information Theory and Automation AS CR},
title = {On best approximation in fuzzy metric spaces},
url = {http://eudml.org/doc/270139},
volume = {51},
year = {2015},
}

TY - JOUR
AU - Abbasi, Naser
AU - Mottaghi Golshan, Hamid
TI - On best approximation in fuzzy metric spaces
JO - Kybernetika
PY - 2015
PB - Institute of Information Theory and Automation AS CR
VL - 51
IS - 2
SP - 374
EP - 386
AB - 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.
LA - eng
KW - best approximation; topology; fuzzy metric spaces; best approximation; topology; fuzzy metric spaces
UR - http://eudml.org/doc/270139
ER -

References

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  1. Beer, G., Pai, D., 10.1080/01630569008816382, Numer. Funct. Anal. Optim. 11 (1990), 5-6, 429-448. Zbl0726.41035MR1079285DOI10.1080/01630569008816382
  2. Chang, S. S., Cho, Y. J., Kang, S. M., Nonlinear Operator Theory in Probabilistic Metric Spaces., Nova Science Publishers Inc, New York 2001. Zbl1080.47054MR2018691
  3. Eldred, A. A., Veeramani, P., 10.1016/j.jmaa.2005.10.081, J. Math. Anal. Appl. 323 (2006), 2, 1001-1006. Zbl1105.54021MR2260159DOI10.1016/j.jmaa.2005.10.081
  4. George, A., Veeramani, P., 10.1016/0165-0114(94)90162-7, Fuzzy Sets and Systems 64 (1994), 3, 395-399. Zbl0843.54014MR1289545DOI10.1016/0165-0114(94)90162-7
  5. George, A., Veeramani, P., 10.1016/s0165-0114(96)00207-2, Fuzzy Sets and Systems 90 (1997), 3, 365-368. Zbl0917.54010MR1477836DOI10.1016/s0165-0114(96)00207-2
  6. Grabiec, M., 10.1016/0165-0114(88)90064-4, Fuzzy Sets and Systems 27 (1998), 3, 385-389. Zbl0664.54032MR0956385DOI10.1016/0165-0114(88)90064-4
  7. Gregori, V., Romaguera, S., 10.1016/s0165-0114(03)00161-1, Fuzzy Sets and Systems 144 (2004), 3, 411-420. Zbl1057.54010MR2061403DOI10.1016/s0165-0114(03)00161-1
  8. Gregori, V., Romaguera, S., 10.1016/s0165-0114(98)00281-4, Fuzzy Sets and Systems 115 (2000), 3, 485-489. Zbl0985.54007MR1781550DOI10.1016/s0165-0114(98)00281-4
  9. Hadžić, O., Pap, E., 10.1007/978-94-017-1560-7, Kluwer Academic Publishers, Dordrecht 2001. Zbl1265.54127MR1896451DOI10.1007/978-94-017-1560-7
  10. Kainen, P. C., 10.1016/j.jfranklin.2004.03.001, J. Franklin Inst. 341 (2004), 4, 391-399. Zbl1075.54013MR2071890DOI10.1016/j.jfranklin.2004.03.001
  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. Zbl1052.54032MR2031823
  12. Kramosil, I., Michálek, J., Fuzzy metrics and statistical metric spaces., Kybernetika 11 (1975), 5, 336-344. Zbl0319.54002MR0410633
  13. Menger, K., 10.1073/pnas.28.12.535, Proc. Nat. Acad. Sci. U. S., A. 28 (1942), 535-537. Zbl0063.03886MR0007576DOI10.1073/pnas.28.12.535
  14. Rodríguez-López, J., Romaguera, S., 10.1016/j.fss.2003.09.007, Fuzzy Sets and Systems 147 (2004), 2, 273-283. Zbl1069.54009MR2089291DOI10.1016/j.fss.2003.09.007
  15. Romaguera, S., Sanchis, M., 10.1016/s0165-0114(00)00085-3, Fuzzy Sets and Systems 124 (2001), 1, 109-115. Zbl0994.54007MR1859783DOI10.1016/s0165-0114(00)00085-3
  16. Sahney, B. E., Singh, S. P., On best simultaneous approximation., In: Approximation Theory III (E. W. Cheney, ed.), 1980, pp. 783-789. Zbl0489.41033MR0602802
  17. Schweizer, B., Sklar, A., 10.2140/pjm.1960.10.313, Pacific J. Math. 10 (1960), 314-334. Zbl0136.39301MR0115153DOI10.2140/pjm.1960.10.313
  18. Shams, M., Vaezpour, S. M., 10.1016/j.chaos.2008.07.009, Chaos Solitons Fractals 41 (2009), 4, 1661-1667. Zbl1200.46072MR2537771DOI10.1016/j.chaos.2008.07.009
  19. Singer, I., 10.1007/978-3-662-41583-2, Springer-Verlag 1970. Zbl0197.38601MR0270044DOI10.1007/978-3-662-41583-2
  20. Vaezpour, S. M., Karimi, F., t-best approximation in fuzzy normed spaces., Iran. J. Fuzzy Syst. 5 (2008), 2, 93-99. Zbl1171.46051MR2432015
  21. Veeramani, P., Best approximation in fuzzy metric spaces., J. Fuzzy Math. 9 (2001), 1, 75-80. Zbl0986.54006MR1822315
  22. Xu, X., 10.1016/0021-9045(88)90008-1, J. Approx. Theory 54 (1988), 3, 322-325. Zbl0653.41030MR0960054DOI10.1016/0021-9045(88)90008-1

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