Urysohn’s lemma, gluing lemma and contraction * mapping theorem for fuzzy metric spaces

Elango Roja; Mallasamudram Kuppusamy Uma; Ganesan Balasubramanian

Mathematica Bohemica (2008)

  • Volume: 133, Issue: 2, page 179-185
  • ISSN: 0862-7959

Abstract

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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.

How to cite

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Roja, Elango, Uma, Mallasamudram Kuppusamy, and Balasubramanian, Ganesan. "Urysohn’s lemma, gluing lemma and contraction$^*$ mapping theorem for fuzzy metric spaces." Mathematica Bohemica 133.2 (2008): 179-185. <http://eudml.org/doc/250517>.

@article{Roja2008,
abstract = {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.},
author = {Roja, Elango, Uma, Mallasamudram Kuppusamy, Balasubramanian, Ganesan},
journal = {Mathematica Bohemica},
keywords = {fuzzy contraction mapping; fuzzy continuous mapping; fuzzy contraction mapping; fuzzy continuous mapping; fixed point},
language = {eng},
number = {2},
pages = {179-185},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Urysohn’s lemma, gluing lemma and contraction$^*$ mapping theorem for fuzzy metric spaces},
url = {http://eudml.org/doc/250517},
volume = {133},
year = {2008},
}

TY - JOUR
AU - Roja, Elango
AU - Uma, Mallasamudram Kuppusamy
AU - Balasubramanian, Ganesan
TI - Urysohn’s lemma, gluing lemma and contraction$^*$ mapping theorem for fuzzy metric spaces
JO - Mathematica Bohemica
PY - 2008
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 133
IS - 2
SP - 179
EP - 185
AB - 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.
LA - eng
KW - fuzzy contraction mapping; fuzzy continuous mapping; fuzzy contraction mapping; fuzzy continuous mapping; fixed point
UR - http://eudml.org/doc/250517
ER -

References

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  1. Metric spaces in fuzzy set theory, J. Math. Anal. Appl. 69 (1979), 205–230. (1979) Zbl0409.54007MR0535292
  2. On some results in fuzzy metric spaces, Fuzzy Sets Syst. 64 (1994), 395–399. (1994) MR1289545
  3. Some theorems in fuzzy metric spaces, J. Fuzzy Math. 3 (1995), 933–940. (1995) MR1367026
  4. On some results of analysis for fuzzy metric spaces, Fuzzy Sets Syst. 90 (1997), 365–368. (1997) MR1477836
  5. On fuzzy metric spaces, Fuzzy Sets Syst. 12 (1984), 215–229. (1984) MR0740095
  6. Fuzzy contraction mapping theorem for fuzzy metric spaces, Bull. Calcutta Math. Soc. 94 (2002), 453–458. (2002) MR1947762
  7. Fuzzy sets, Inform and Control 8 (1965), 338–353. (1965) Zbl0139.24606MR0219427
  8. Fuzzy pseudo metric spaces, J. Math. Anal. Appl. 86 (1982), 74–95. (1982) 

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