BEST PROXIMITY POINT RESULTS FOR FUZZY Z-PROXIMAL CONTRACTIONS IN FUZZY METRIC SPACES
DOI:
https://doi.org/10.46754/jmsi.2024.12.006Keywords:
Fuzzy Z-proximal contractions, Best proximity points, Fuzzy metric spaces, Fuzzy psi-proximal contractionsAbstract
In this manuscript, we introduce the concept of fuzzy -proximal contractions in the framework of fuzzy metric spaces. Additionally, we present novel findings regarding the existence and the uniqueness of best proximity points for such contractions in complete fuzzy metric spaces. These new findings extend and generalize certain results in the existing literature. Examples are included to support our findings.
References
Saleem, N., Javed, K., Uddin, F., Ishtiaq U., Ahmed, K., Abdeljawad, T., & Alqudah, M. A. (2023). Unique solution of integral equations via intuitionistic extended fuzzy-metriclike spaces. Computer Modeling in Engineering and Sciences, 135(1), 109-131. https://doi.org/10.32604/cmes.2022.021031
Gopal, D., & Moreno, J. M. (2023). Recent advances and applications of fuzzy metric fixed point theoryi. CRC Press.
Younis, M., & Abdau, A. A. N. (2024). Novel fuzzy contractions and applications to engineering science. Fractal and Fractional, 8(1), Article 28. https://doi.org/10.3390/fractalfract8010028
Younis, M., Ahmad, H., Chen, L., & Han, M. (2023). Computation and convergence of fixed points in graphical spaces with an application to elastic beam deformations. Journal of Geometry and Physics, 192, Article 104955. https://doi.org/10.1016/j.geomphys.2023.104955
Agarwal, R. P., Meehan, M., & O’regan, D. (2001). Fixed point theory and applications. Cambridge University Press.
Gopal, D., Kumam, P., & Abbas, M. (2017). Background and recent developments of metric fixed-point theory. CRC Press.
Saleem, N., Ali, B., Abbas, M., & Raza, Z. (2015). Fixed points of Suzuki type generalized multivalued mappings in fuzzy metric spaces with applications. Fixed Point Theory and Applications, 2015, Article 36. https://doi.org/10.1186/s13663-015-0284-7
Shukla, S., Rodríguez-López, R., & Abbas, M. (2018). Fixed point results for contraction mappings in complex valued fuzzy metric spaces. Fixed Point Theory, 19(2), 751-774. https://doi.org/10.24193/fpt-ro.2018.2.56
Ali, M. U., Ansari, A. H., Khammahawong, K., & Kumam, P. (2017). Best proximity point theorems for generalized --proximal contractions (pp. 341-352). In Anh, L., Dong, L., Kreinovich, V., & Thach, N. (Eds.), Econometrics for Financial Applications, Springer. https://doi.org/10.1007/978-3-319-73150-6_27
Gabeleh, M., & Plebaniak, R. (2018). Global optimality results for multivalued non-self mappings in -metric space. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A: Mathemáticas, 112(2), 347-360. https://doi.org/10.1007/s13398-017-0383-x
Kirk, W. A. (2007). Some recent results in metric fixed point theory. Journal of Fixed Point Theory and Applications, 2(2), 195-207. https://doi.org/10.1007/s11784-007-0031-8
Sadiq Basha, S., & Veeramani, P. (1997). Best proximity pairs and best approximations. Acta Scientiarum Mathematicarum, 63(1), 289-300.
Menger, K. (1942). Satistical Metric. Proceedings of the National Academy of Sciences of the United States of America, 28, 535-357.
Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8(3), 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X
Kramosil, I., & Michálek, J. (1975). Fuzzy metric and statistical metric spaces. Kybernetika, 11(5), 326-334.
George, A., & Veeramani, P. (1994). On some results on fuzzy metric spaces. Fuzzy Sets and Systems, 64(3), 395-399. https://doi.org/10.1016/0165-0114(94)90162-7
Vetro, C., & Salimi, P. (2013). Best proximity point results in non-Archimedean fuzzy metric spaces. Fuzzy Information and Engineering, 5(4), 417-429. https://doi.org/10.1007/s12543-013-0155-z
Wong, K. S., Salleh, Z., & Akhadkulov, H. (2024). Fuzzy metric spaces: Optimizing coincidence and proximity points. Contemporary Mathematics, 5(2), 1146-1164. https://doi.org/10.37256/cm.5220242655
Shukla, S., Gopal, D., & Sintunavarat, W. (2018). A new class of fuzzy contractive mappings and fixed point theorems. Fuzzy Sets and Systems, 350(1), 85-94. https://doi.org/10.1016/j.fss.2018.02.010
Gopal, D., & Martínez-Moreno, J. (2021). Suzuki type fuzzy -contractive mappings and fixed points in fuzzy metric spaces. Kybernetika, 57(6), 908-921. https://doi.org/10.14736/kyb-2021-6-0908
Schweizer, B., & Sklar, A. (1960). Statistical metric spaces. Pacific Journal of Mathematics, 10(1), 314-334.
Grabiec, M. (1988). Fixed points in fuzzy metric spaces. Fuzzy Sets and Systems, 27(3), 385-389. https://doi.org/10.1016/0165-0114(88)90064-4
Saleem, N., Abbas, M., & Raza, Z. (2016). Optimal coincidence best approximation solution in non-Archimedean fuzzy metric spaces. Iranian Journal of Fuzzy Systems, 13(3), 113-124. https://doi.org/10.22111/IJFS.2016.2433
Saleem, N., Abbas, M., & Sohail, K. (2021). Approximate fixed point results for -type and-type fuzzy contractive mappings in -fuzzy metric spaces. Malaysian Journal of Mathematical Sciences, 15(2), 267-281.
Jain, S., & Radenović, S. (2023). Interpolative fuzzy -contraction with its application to Fredholm non-linear integral equation. Gulf Journal of Mathematics, 14(1), 84-98. https://doi.org/10.56947/gjom.v14i1.1009
Younis, M., Chen, L., & Singh, D. (2024). Recent developments in fixed point theory: Theoretical foundations and real-world applications. Springer Singapore.
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