Fixed point theorems for single valued α-ψ-mappings in fuzzy metric spaces

Abstract

This article is the forward result of α-admissible and (α,ψ)-contractive mappings in fuzzy metric spaces. We establish new theorem for such contractions to find fixed point in fuzzy metric space. Our Theorem is generalizations of some interesting outputs in metric spaces. Moreover, an example and application to ordinary differential equations are also elaborated to verify the result of the theorem.

Keywords

• fixed points,(α,ψ)-weak contraction condition,altering distance functon,fuzzy metric spaces

References

1. Doric, D., Common fixed points for generalized (ψ,φ) weak contraction, Applied Mathematics Letters, 22, (2009) 1896--1900.
2. George, A. and Veeramani, P., On some results in fuzzy metric spaces, Fuzzy Sets Syst., 64, (1994) 395--399.
3. Kramosil, I. and Michalek, J., Fuzzy metric and statistical metric spaces, Kybernetica, 11 (5), (1975) 336-344.
4. Mihet, D., Fuzzy ψ-contractive mapping in non-archimedean fuzzy metric spaces, Fuzzy sets Syst., 159 , (2008) 739-744.
5. Murthy, P.P., Tas, K. and Patel, U.D., Common fixed point theorems for generalized (ψ,φ) weak contraction condition in complete metric spaces, Journal of Inequalities and Applications Applied Mathematics, 139, (2015) 14 pages.
6. Schweizer, B., and Sklar, A., Probabilistic metric spaces, Elsvier, North Holand, 1983.
7. Zadeh, L.A., Fuzzy sets, Inform. and Control 8, (1965) 338--353.
8. Gregori, V., Sapena, A., On Fixed Point Theorems in fuzzy metric space, Fuzzy Sets and Systems, 125, (2002) 245--252.

9. Samet, B., Vetro, C., Vetro, P., Fixed point theorem for α-ψ contractive type mappings, Nonlinear Anal., 75, (2012) 2154 -- 2165.
10. Salimi, P., Latif, A., Hussian, N., Modified α-ψ Contractive Mappings with Applications, Fixed Point Theory Appl., Article ID 151 (2013).
11. Hong, S., Fixed Points for Modified Fuzzy ψ-Contractive Set-valued Mappings in fuzzy metric space, Fixed Point Theory and Applications, 1(12), (2014) 11-pages. Doi:10.1186/1687-1812-2014-12.
12. Saha, P., Choudhury, B.S., Das, P., A new contractive mapping principle in fuzzy metric spaces, Boll. Unione Mat. Ital., DOI 10.1007/s40574-015-0044-y.
13. Saini, R.K., Gupta, V., Singh, S.B., Fuzzy Version of Some Fixed Points Theorems On Expansion Type Maps in Fuzzy Metric Space, Thai Journal of Mathematics, 5(2), (2007) 245--252.
14. Gupta, V., Saini, R.K., Mani, N., Tripathi, A.K., Fixed point theorems by using control function in fuzzy metric spaces, Cogent Mathematics, 2(1), (2015).
15. Gupta, V., Kanwar, A., V-Fuzzy metric space and related fixed point theorems, Fixed Point Theory and Applications, 51,(2016) DOI: 10.1186/s13663-016-0536-1.
16. Gupta, V., Verma, M. and Gulati, N., Unique fixed point results for sequence of self mappings in generalized fuzzy metric spaces, Journal of Uncertain Systems, 10(2), (2016) 108--113.
17. Gupta, V., Verma, M., Khan, M.S., Common Fixed Point in Generalized Fuzzy Metric Spaces, The Journal of Fuzzy Mathematics, Los Angeles, 25(3), (2017) 533-541.
18. Gupta, V., Saini, R.K., Kanwar, A., Some coupled fixed point results on modified intuitionistic fuzzy metric spaces and application to integral type contraction, Iranian Journal of Fuzzy Systems, 14(5), (2017) 123--137.