Solving Integral Equation Via Fixed Point Theorems in Generalized $N$-Fuzzy Metric Spaces
DOI:
https://doi.org/10.5890/DNC.2025.12.007Abstract
In the present paper, we announced a new notion of ``generalized $N$-fuzzy metric spaces" which explores a more broad view of fuzzy metric spaces mentioned in the reviewed literatures. A fixed point theorem in the setting of Generalized $N$-fuzzy metric space via fuzzy $n$-Banach Contraction mapping was proved. Finally, we demonstrated an application of main results in solving integral equation.References
[1] Banach, S. (1922), Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fundamenta Mathematicae, 3(1), 133-181.
[2] Berinde, V. (2003), On the approximation of fixed points of weak contractive mappings, Carpathian Journal of Mathematics, 9(1), 7-22.
[3] Boyd, W. and Wong, J. (1969), On nonlinear contractions, Proceedings of the American Mathematical Society, 20(2), 458-464.
[4] Ciric, L. (1974), A generalization of Banach contraction principle, Proceedings of the American Mathematical Society, 45(2), 267-273.
[5] Piri, H. and Kumam, P. (2014), Some fixed point theorem concerning $F$-contraction in complete metric spaces, Fixed Point Theory and Applications, 210(1), 1-11.
[6] Suzuki, T. (2008), A generalized Banach contraction principle that characterizes metric completeness, Proceedings of the American Mathematical Society, 136(5), 1861-1869.
[7] Ashref, M., Ali, R., and Hussain, N. (2020), New fuzzy fixed point results in generalized fuzzy metric spaces with applications to integral equations, IEEE Access, 8, 91653-91660.
[8] Alexander, S. (2018), George-Veeramani fuzzy metric revised, Axioms, 7(60), 2-7.
[9] Erceg, M. (1979), Metric spaces in fuzzy set theory, Journal of Mathematical Analysis and Applications, 69(1), 205-230.
[10] George, A. and Veeramani, P. (1994), On some results of fuzzy metric spaces, Fuzzy Sets and Systems, 64(3), 395-399.
[11] Gregori, V., Minana, J., and Miravet, D. (2019), Extended fuzzy metrics and fixed point theorems, Mathematics, 7(303), 1-14.
[12] Kider, J. (2015), Completion of standard fuzzy metric spaces, Open Science Journal of Mathematics and Applications, 3(2), 19-25.
[13] Kramosil, I. and Michalek, J. (1975), Fuzzy metric and statistical metric space, Kybernetika, 11(5), 326-334.
[14] Sedghi, S. and Shobe, N. (2006), Fixed point theorem in M-fuzzy metric spaces with property (E), Advances in Fuzzy Mathematics, 1(1), 55-65.
[15] Ansari, Z.K., Shrivastava, R., Ansari, G., and Garg, A. (2011), Some fixed point theorems in fuzzy 2-metric and fuzzy 3-metric spaces, International Journal of Contemporary Mathematical Sciences, 6(46), 2291-2301.
[16] Gupta, V. and Kanwar, A. (2016), $V$-fuzzy metric space and related fixed point theorems, Fixed Point Theory and Applications, 2016, 1-17.
[17] Gopal, D., Sintunavarat, W., Ranadive, A.S., and Shukla, S. (2023), The investigation of k-fuzzy metric spaces with the first contraction principle in such spaces, Soft Computing, 27(16), 11081-11089.
[18] Schweizer, B. and Sklar, A. (1960), Statistical metric spaces, Pacific Journal of Mathematics, 10(1), 314-334.
[19] Grabiec, M. (1988), Fixed points in fuzzy metric spaces, Fuzzy Sets and Systems, 27(3), 385-389.
[20] Bag, T. (2012), Some results on $D^{ast}$-metric spaces, International Journal of Mathematics and Scientific Computing, 2(1), 29-33.
[21] Beg, I., Gopal, D., Dosenovic, T., and Rakic, D. (2018), $alpha$-Type fuzzy $mathcal{H}$-contractive mappings in fuzzy metric spaces, Fixed Point Theory, 19(2), 463-474.
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