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FIXED POINT THEOREM USING A NEW CLASS OF FUZZY CONTRACTIVE MAPPINGS

Year 2018, Volume: 1 Issue: 2, 148 - 154, 31.07.2018

Said Melliani , Abdelahamid Moussaoui

Abstract

In this paper we introduce a new class of fuzzy contractive mapping and we show that such a class unify and generalize several existing concepts in the literature. We establish xed point theorem for such mappings in complete strong fuzzy metric spaces and we give an illustrative example

Keywords

Fuzzy mappings fixed point theorem

References

  • M. Grabiec, Fixed points in fuzzy metric spaces, Fuzzy Sets Syst. 27 (1988) 385-389.
  • M. Edelstein, On fixed and periodic points under contractive mappings, J. Lond. Math. Soc. 37 (1962) 74-79.
  • A. George, P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets Syst. 64 (1994) 395-399.
  • V. Gregori and A. Sapena, On fixed-point theorems in fuzzy metric spaces, Fuzzy Sets and Systems 125 (2002), 245-252.
  • V. Gregori, S. Morillas, A. Sapena, Examples of fuzzy metrics and applications, FuzzyS ets and Systems 170 (2011) 95-111.
  • V. Gregori, J.-J. Minana, Some remarks on fuzzy contractive mappings, Fuzzy Sets Syst. 251 (2014) 101-103.
  • V. Radu, Some remarks on the probabilistic contractions on fuzzy Menger spaces, Automat. Comput. Appl. Math. 11 (2002) 125-131.
  • B. Schweizer, A. Sklar, Statistical metric spaces, Pacific. J. Math. 10 (1960) 313-334.
  • D. Mihet, On fuzzy contractive mappings in fuzzy metric spaces, Fuzzy Sets and Systems 158 (2007) 915-921.
  • D. Mihet, Fuzzy \psi-contractive mappings in non-Archimedean fuzzy metric spaces, Fuzzy Sets and Systems 159 (2008) 739-744.
  • D. Wardowski, Fuzzy contractive mappings and fixed points in fuzzy metric spaces, Fuzzy Sets Syst. 222 (2013) 108-114.
  • I. Kramosil, J. Michalek, Fuzzy metric and statistical metric spaces, Kybernetica 15 (1975) 326-334.
  • Ciric, L.: Some new results for Banach contractions and Edelstein contractive mappings on fuzzy metric spaces. Chaos Solitons Fractals 42, 146-154 (2009).
  • Shen, Y., Qiu, D., Chen,W.: Fixed point theorems in fuzzy metric spaces. Appl. Math. Lett. 25, 138-141 (2012).
  • Roldan, A., Martinez, J., Roldan, C., Cho,Y.J.: Multidimensional coincidence point results for compatible mappings in partially ordered fuzzy metric spaces. Fuzzy Sets Syst. 251, 71-82 (2014).

Year 2018, Volume: 1 Issue: 2, 148 - 154, 31.07.2018

Said Melliani , Abdelahamid Moussaoui

Abstract

References

  • M. Grabiec, Fixed points in fuzzy metric spaces, Fuzzy Sets Syst. 27 (1988) 385-389.
  • M. Edelstein, On fixed and periodic points under contractive mappings, J. Lond. Math. Soc. 37 (1962) 74-79.
  • A. George, P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets Syst. 64 (1994) 395-399.
  • V. Gregori and A. Sapena, On fixed-point theorems in fuzzy metric spaces, Fuzzy Sets and Systems 125 (2002), 245-252.
  • V. Gregori, S. Morillas, A. Sapena, Examples of fuzzy metrics and applications, FuzzyS ets and Systems 170 (2011) 95-111.
  • V. Gregori, J.-J. Minana, Some remarks on fuzzy contractive mappings, Fuzzy Sets Syst. 251 (2014) 101-103.
  • V. Radu, Some remarks on the probabilistic contractions on fuzzy Menger spaces, Automat. Comput. Appl. Math. 11 (2002) 125-131.
  • B. Schweizer, A. Sklar, Statistical metric spaces, Pacific. J. Math. 10 (1960) 313-334.
  • D. Mihet, On fuzzy contractive mappings in fuzzy metric spaces, Fuzzy Sets and Systems 158 (2007) 915-921.
  • D. Mihet, Fuzzy \psi-contractive mappings in non-Archimedean fuzzy metric spaces, Fuzzy Sets and Systems 159 (2008) 739-744.
  • D. Wardowski, Fuzzy contractive mappings and fixed points in fuzzy metric spaces, Fuzzy Sets Syst. 222 (2013) 108-114.
  • I. Kramosil, J. Michalek, Fuzzy metric and statistical metric spaces, Kybernetica 15 (1975) 326-334.
  • Ciric, L.: Some new results for Banach contractions and Edelstein contractive mappings on fuzzy metric spaces. Chaos Solitons Fractals 42, 146-154 (2009).
  • Shen, Y., Qiu, D., Chen,W.: Fixed point theorems in fuzzy metric spaces. Appl. Math. Lett. 25, 138-141 (2012).
  • Roldan, A., Martinez, J., Roldan, C., Cho,Y.J.: Multidimensional coincidence point results for compatible mappings in partially ordered fuzzy metric spaces. Fuzzy Sets Syst. 251, 71-82 (2014).
There are 15 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

Said Melliani 0000-0002-5150-1185

Abdelahamid Moussaoui This is me

Publication Date July 31, 2018
Submission Date May 15, 2018
Acceptance Date August 5, 2018
Published in Issue Year 2018 Volume: 1 Issue: 2

Cite

APA Melliani, S., & Moussaoui, A. (2018). FIXED POINT THEOREM USING A NEW CLASS OF FUZZY CONTRACTIVE MAPPINGS. Journal of Universal Mathematics, 1(2), 148-154.
AMA Melliani S, Moussaoui A. FIXED POINT THEOREM USING A NEW CLASS OF FUZZY CONTRACTIVE MAPPINGS. JUM. July 2018;1(2):148-154.
Chicago Melliani, Said, and Abdelahamid Moussaoui. “FIXED POINT THEOREM USING A NEW CLASS OF FUZZY CONTRACTIVE MAPPINGS”. Journal of Universal Mathematics 1, no. 2 (July 2018): 148-54.
EndNote Melliani S, Moussaoui A (July 1, 2018) FIXED POINT THEOREM USING A NEW CLASS OF FUZZY CONTRACTIVE MAPPINGS. Journal of Universal Mathematics 1 2 148–154.
IEEE S. Melliani and A. Moussaoui, “FIXED POINT THEOREM USING A NEW CLASS OF FUZZY CONTRACTIVE MAPPINGS”, JUM, vol. 1, no. 2, pp. 148–154, 2018.
ISNAD Melliani, Said - Moussaoui, Abdelahamid. “FIXED POINT THEOREM USING A NEW CLASS OF FUZZY CONTRACTIVE MAPPINGS”. Journal of Universal Mathematics 1/2 (July 2018), 148-154.
JAMA Melliani S, Moussaoui A. FIXED POINT THEOREM USING A NEW CLASS OF FUZZY CONTRACTIVE MAPPINGS. JUM. 2018;1:148–154.
MLA Melliani, Said and Abdelahamid Moussaoui. “FIXED POINT THEOREM USING A NEW CLASS OF FUZZY CONTRACTIVE MAPPINGS”. Journal of Universal Mathematics, vol. 1, no. 2, 2018, pp. 148-54.
Vancouver Melliani S, Moussaoui A. FIXED POINT THEOREM USING A NEW CLASS OF FUZZY CONTRACTIVE MAPPINGS. JUM. 2018;1(2):148-54.
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