Compatibility of type (β) and Common fixed point theorem in intuitionistic fuzzy metric space

Preeti Sengar; Suman Jain; Aklesh Paria; V.H.Badshah

doi:https://doi.org/10.14445/22315373/IJMTT-V38P509

International Journal of Mathematics Trends and Technology

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Volume 38 | Number 1 | Year 2016 | Article Id. IJMTT-V38P509 | DOI : https://doi.org/10.14445/22315373/IJMTT-V38P509

Compatibility of type (β) and Common fixed point theorem in intuitionistic fuzzy metric space

Preeti Sengar, Suman Jain, Aklesh Paria, V.H.Badshah

Abstract

In this paper, we prove a common fixed point theorem by using compatibility of type (β) in intuitionistic fuzzy metric space. Our result extends and generalizes the result of Cho [4].

Keywords

Common fixed points, fuzzy metric space, compatible maps, and compatible maps of type (β).

References

[1]Alaca, C. Turkoglu, D. and Yildiz, C., Fixed point in intuitionistic fuzzy metric spaces, Chaos, Solitons and Fractals 29(2006), 1073- 1078.
[2] Alaca, C., Altun, I. and Turkoglu, D. On compatible mappings of type (I) and type (II) in Intuitionistic fuzzy metric spaces, Commun. Korean Math.Soc., 23(3) (2008) 427-446.
[3] Cho, S. H., On Common fixed point theorems in fuzzy metric spaces, J. Appl. Math. & Computing Vol.20 (2006), No.1-2, 523-533.
[4]George, A. and Veeramani , P., On some results in fuzzy metric spaces, fuzzy sets and system, 64 (1994),395-399.
[5]Kramosil, O., Michalek, J., Fuzzy metric and Statistical metric space, Kybernetika, 11(1975), 326-334.
[6] Jungck, G., Compatible mappings and common fixed points, Internet. J. Math. and Sci.9(4) (1986) 771-779.
[7] Jungck, G., Murthy, P. P. and Cho, Y.J., Compatible mappings of type (A) and common fixed points, Math. Japonica, 38(1993) 381-390.
[8]Schweizer, B. and Sklar, A., Statistical metric space, Pacific Journal Math. 10(1960),314-334.
[9] Singh, B. and Chauhan, M.S., Common fixed points of compatible maps in Fuzzy metric spaces, Fuzzy Sets and Systems 115(2000) 471-475.
[10]Turkoglu, D., Alaca, C., and Yildiz, C., Compatible maps and Compatible maps of types (β) and ( in intuitionistic fuzzy metric spaces, Demonstratio Math. 39(2006),671-684.
[11] Zadeh, L.A., Fuzzy Sets, Inform and Control 89(1965), 338-353.

Citation :

Preeti Sengar, Suman Jain, Aklesh Paria, V.H.Badshah, "Compatibility of type (β) and Common fixed point theorem in intuitionistic fuzzy metric space," International Journal of Mathematics Trends and Technology (IJMTT), vol. 38, no. 1, pp. 58-69, 2016. Crossref, https://doi.org/10.14445/22315373/IJMTT-V38P509