Banach's and Kannan's fixed point results in fuzzy 2-metric spaces


  • Binod Chandra Tripathy Institution of Advanced Study in Science and Technology.
  • Sudipta Paul Gauhati University.
  • Nanda Ram Das Gauhati University.



Fuzzy 2-metric space, Hadzic type tnorm, Weakly compatible mapping, ψ-function.


In this paper we establish two common fixed point theorems in fuzzy 2-metric spaces. These theorems are generalizations of the Banach Contraction mapping principle and the Kannan's fixed point theorem respectively in fuzzy 2-metric spaces.

Author Biographies

Binod Chandra Tripathy, Institution of Advanced Study in Science and Technology.

Mathematical Science Division; Paschim Boragaon,Garchuk; Guwahati-781035, ASSAM.

Sudipta Paul, Gauhati University.

Department of Mathematics, Guwahati-781014; ASSAM.

Nanda Ram Das, Gauhati University.

Department of Mathematics, Guwahati-781014; ASSAM.


[1] B. S. Choudhury and K.Das, Fixed points of generalized Kannan type mapping in generalized Menger spaces, commun Korean Math, Soc. 24(4), pp. 529-537, (2009).

[2] B. S Choudhury K.Das and P.Das, Extensions of Banach’s and Kannan’s results in Fuzzy metric Space. Hacettepe Journal of Mathematics and Statistics, 39(1), pp. 1-9, (2009).

[3] B. S. Choudhury and A. Kundu, A common fixed point result in fuzzy metric spaces using altering distances, J. Fuzzy Math. 18 (2), pp. 517- 52, (2010).

[4] L. Ciric, Some new results for Banach contradiction and Edelstein contractive mappings on fuzzy metric spaces, chaos solitons fractals 42(1), pp. 146-154, (2009).

[5] S. Gahler, Linear 2-normierte Raume, Math. Nachr, 28 pp. 1-43, (1964).

[6] S. Gahler, U ber 2-Banach Raume, Math. Nachr. 42, pp. 335-347, (1969).

[7] A. George and P. Veeramani, On some results in fuzzy metric spaces, Fuzzy sets and systems 64(3), pp. 395-399, (1994).

[8] O. Hadzic and E. Pap, Fixed Point Theory in Probabilistic Metric Space, Kluwer Academic Publishers, Dordrecht, (2001).

[9] S. Heipern, Fuzzy mapping and fixed point theorems, J. Maths, Anal. Appl. 83, pp. 565-569, (1981).

[10] O. Kramosil and J. Michalek: Fuzzy metric and statistical metric spaces, Kybernelika, 11, pp. 326-334, (1975).

[11] B. C. Tripathy and A. Baruah, Lacunary statistically convergent and lacunary strongly convergent generalized difference sequences of fuzzy real numbers, Kyungpook Math. J., 50(4), pp. 565-574, (2010).

[12] B. C. Tripathy and A. Baruah, M.Et and M. Gungor, On almost statistical convergence of new type of generalized difference sequence of fuzzy numbers, Iranian Jour. Sci. Tech., Trans. A : Sci., 36 (2), pp. 147-155, (2012).

[13] B. C. Tripathy and S. Borgogain, Some classes of difference sequence spaces of fuzzy real numbers defined by Orlicz function; Adv. Fuzzy Syst., 2011, Article ID216414, 6 pages (2011).

[14] B. C. Tripathy and A. J. Dutta, Lacunary bounded variation sequence of fuzzy real numbers, Jour. Intell. Fuzzy Syst., 24 (1), pp. 185-189, (2013).

[15] B. C. Tripathy and S. Debnath, γ-open sets and γ-continuous mappings in fuzzy bitopological spaces, Jour. Intell. Fuzzy Syst., 24(3), pp. 631-635, (2013).

[16] B. C. Tripathy and G.C. Ray, On Mixed fuzzy topological spaces and countability, Soft Comput., 16 (10), pp. 1691-1695, (2012).

[17] B. C. Tripathy and B. Sarma, On I-convergent double sequences of fuzzy real numbers; Kyungpook Math. J., 52 (2), pp. 189-200, (2012).

[18] S. Sharma, On fuzzy metric space, Southeast Asian Bulletin of Mathematics, 26, pp. 133-145, (2002).

How to Cite

B. Chandra Tripathy, S. Paul, and N. Ram Das, “Banach’s and Kannan’s fixed point results in fuzzy 2-metric spaces”, Proyecciones (Antofagasta, On line), vol. 32, no. 4, pp. 359-375, 1.




Most read articles by the same author(s)