On Generalized (Ψ,φ)-Almost Weakly Contractive Maps in Generalized Fuzzy Metric Spaces

Abstract

In this paper, we come out with the approach of generalized  (Ψ,φ)-almost weakly contractive maps in the context of generalized fuzzy metric spaces. We prove theorem to show the existence of a fixed point and also provide an example in support to our result.

Keywords

• (Ψ,φ)-almost weakly contractive map,Fuzzy metric space,Generalized fuzzy metric spaces

References

1. [1] Atanassov, K., Intuitionistic fuzzy sets, Fuzzy, Sets and Systems 20 (1986) 87–96.
2. [2] George, A. and Veeramani, P., On some results in fuzzy metric spaces, Fuzzy sets and Systems, (1994). 395–399.
3. [3] Kramosil, I. and Michalek, J., Fuzzy metric and statistical metric space, Kybernetika, 11(1975), 326-334.
4. [4] Sun, G. and Yang, K., Generalized fuzzy metric spaces with properties, Research Journal of Applied Sciences Eng. and Technology, Vol.2, (7), (2010), 673-678.
5. [5] Babu, G. V. R., Dasari Ratna babu, Kanuri Nageswara Rao, Bendi Venkata Siva Kumar, Fixed points of (Ψ,φ)-almost weakly contractive maps in G- metric Spaces, Applied Mathematical E-Notes 14 (2014), 69- 85.
6. [6] Berinde, V., Approximating fixed points of weak contractions using the picard Iteration, Nonlinear Anal. Forum, 9 (2004), 43- 53.
7. [7] Doric, D., Common fixed point for generalized (Ψ,φ) - weakly contractions, Appl. Math. Letter., 22 (2009), 1896-1900.
8. [8] Dutta, P. N. and Choudhury B. S., A generalization of contraction principle in metric spaces, Fixed point Theory and Appl., (2008), Article ID 406368.

9. [9] Harjani, J. and Sadarangani, K., Fixed point theorems for weakly contractive mappings in partially ordered sets, Nonlinear Analy., 71 (2009) 3403-3410.
10. [10] Manthena P., Rangamma, M., Fixed points of of (Ψ,φ)-lmost weakly contractive maps in Fuzzy metric spaces, Advanced Fixed point theory, 6 (2016), No.4, 387-396.
11. [11] Rhoades, B. E., some theorems on weak contractive maps, Nonlinear Anal. 47(2001), 2683- 2693.
12. [12] Saha, P., A weak contraction in G- Complete Fuzzy metric space, Intern. J. Fuzzy Mathematical Archive 3 (2013), 100- 103.
13. [13] Schweizer, B. and Sklar, A., Statistical metric spaces, Pacific Journal of Math., 10 (1960), 313.
14. [14] Zang, Q. and Song, Y., Fixed point theory for generalized φ–weak contractions, Appl. Math. Letter, 22 (2009), 75-78.
15. [15] Zadeh, L. A, Fuzzy sets, Infor. and Control., (1965), 8338 – 353.