FIXED POINT THEOREM USING A NEW CLASS OF FUZZY CONTRACTIVE MAPPINGS

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

1. M. Grabiec, Fixed points in fuzzy metric spaces, Fuzzy Sets Syst. 27 (1988) 385-389.
2. M. Edelstein, On fixed and periodic points under contractive mappings, J. Lond. Math. Soc. 37 (1962) 74-79.
3. A. George, P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets Syst. 64 (1994) 395-399.
4. V. Gregori and A. Sapena, On fixed-point theorems in fuzzy metric spaces, Fuzzy Sets and Systems 125 (2002), 245-252.
5. V. Gregori, S. Morillas, A. Sapena, Examples of fuzzy metrics and applications, FuzzyS ets and Systems 170 (2011) 95-111.
6. V. Gregori, J.-J. Minana, Some remarks on fuzzy contractive mappings, Fuzzy Sets Syst. 251 (2014) 101-103.
7. V. Radu, Some remarks on the probabilistic contractions on fuzzy Menger spaces, Automat. Comput. Appl. Math. 11 (2002) 125-131.
8. B. Schweizer, A. Sklar, Statistical metric spaces, Pacific. J. Math. 10 (1960) 313-334.

9. D. Mihet, On fuzzy contractive mappings in fuzzy metric spaces, Fuzzy Sets and Systems 158 (2007) 915-921.
10. D. Mihet, Fuzzy \psi-contractive mappings in non-Archimedean fuzzy metric spaces, Fuzzy Sets and Systems 159 (2008) 739-744.
11. D. Wardowski, Fuzzy contractive mappings and fixed points in fuzzy metric spaces, Fuzzy Sets Syst. 222 (2013) 108-114.
12. I. Kramosil, J. Michalek, Fuzzy metric and statistical metric spaces, Kybernetica 15 (1975) 326-334.
13. Ciric, L.: Some new results for Banach contractions and Edelstein contractive mappings on fuzzy metric spaces. Chaos Solitons Fractals 42, 146-154 (2009).
14. Shen, Y., Qiu, D., Chen,W.: Fixed point theorems in fuzzy metric spaces. Appl. Math. Lett. 25, 138-141 (2012).
15. 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).