| Title:
|
Exploring fixed point results in fuzzy $\mathscr {F}$-metric spaces with an application to satellite web coupling problem (English) |
| Author:
|
Barman, Dipti |
| Author:
|
Das, Abhishikta |
| Author:
|
Bag, Tarapada |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 (print) |
| ISSN:
|
1805-949X (online) |
| Volume:
|
62 |
| Issue:
|
2 |
| Year:
|
2026 |
| Pages:
|
237-256 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this article, we study some basic properties of $ \mathscr{F}$-compactness and $ \mathscr{F}$-totally boundedness in fuzzy $ \mathscr{ F } $-metric spaces. We establish a fixed-point theorem in this setting and apply it to the satellite web coupling problem. To justify the fixed-point result, a counterexample and a graphical illustration of the contraction condition are presented. Furthermore, a numerical illustration is provided to justify the applicability of the result, where the successive iterates and the decay of the sup-norm error demonstrate the effectiveness of the proposed approach. (English) |
| Keyword:
|
t-norm |
| Keyword:
|
fuzzy $\mathscr {F}$-metric space |
| Keyword:
|
fixed point |
| Keyword:
|
ODE |
| Keyword:
|
satellite web coupling problem |
| MSC:
|
46S40 |
| MSC:
|
54H27 |
| MSC:
|
55M20 |
| DOI:
|
10.14736/kyb-2026-2-0237 |
| . |
| Date available:
|
2026-05-21T16:10:15Z |
| Last updated:
|
2026-05-21 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/153633 |
| . |
| Reference:
|
[1] Bag, T.: Some results on $ D^\star $-fuzzy metric spaces..Int. J. Math. Sci. Computing 2 (2012), 29-33. |
| Reference:
|
[2] Milles, O. Barkat S., Latreche, A.: On the completeness and compactness with Eldestein fixed point theorem in standard Intuitionistic Fuzzy Metric Spaces..Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 17 (2024), 2440003. |
| Reference:
|
[3] Das, A., Barman, D., Bag, T.: A new generalization of George \& Veeramani type fuzzy metric space..Probl. Anal. Issues Anal. 13 (2024), 23-42. |
| Reference:
|
[4] Din, F. U., Alshaikey, S., Ishtiaq, U., Dinn, M., Sessa, S.: Single and multi-valued ordered-theoretic perov fixed-point results for $ \theta $-contraction with application to nonlinear system of matrix equations..Mathematics 12 (2024), 1302. |
| Reference:
|
[5] Din, F. U., Din, M., Ishtiaq, U., Sessa, S.: Perov fixed-point results on $ F $-contraction mappings equipped with binary relation..Mathematics 11 (2023), 238. |
| Reference:
|
[6] George, A., Veeramani, P.: On some results in fuzzy metric spaces..Fuzzy Sets Syst. 64 (1994), 395-399. Zbl 0843.54014, |
| Reference:
|
[7] Gregori, V., Sapena, A.: On fixed-point theorems in fuzzy metric spaces..Fuzzy Sets Syst. 125 (2002), 245-252. |
| Reference:
|
[8] Guo, L., Alshaikey, S., Alshejari, A., Din, M., Ishtiaq, U.: Numerical algorithm for coupled fixed points in normed spaces with applications to fractional differential equations and economics..Fractal Fractional 9 (2025), 37. |
| Reference:
|
[9] Ishtiaq, U., Din, M., Rohen, Y., Alnowibet, K. A., Popa, I.: Certain fixed-point results for $(\textit{e}, \Psi, \Phi)$-enriched weak contractions via theoretic order with applications..Axioms { \mi 14 } (2025), 135. |
| Reference:
|
[10] Amanathulla, J. Khatun S., Pal, M.: A comprehensive study on m-polar picture fuzzy graphs and its application..Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 18 (2024), 2450016. |
| Reference:
|
[11] Klir, G. J., Yuan, B.: Fuzzy Sets and Fuzzy Logic..Printice-Hall of India Private Limited, New Delhi-110001, 1997. |
| Reference:
|
[12] Kramosil, I., Michálek, J.: Fuzzy metrics and statistical metric spaces..Kybernetika 11 (1975), 336-344. Zbl 0319.54002 |
| Reference:
|
[13] Mihet, D.: Fuzzy $ \psi $-contractive mappings in non-Archimedean fuzzy metric spaces..Fuzzy Sets Syst. 159 (2008), 739-744. |
| Reference:
|
[14] Nadaban, S.: Fuzzy $ b $-metric space..Int. J. Computers Commun.Control 11 2016, 273-281. |
| Reference:
|
[15] Oner, T., Kandemir, M. B., Tanay, B.: Fuzzy cone metric spaces..J. Nonlinear Sci. Appl. 8 (2015), 610-616. |
| Reference:
|
[16] Sedghi, S., Shobe, N.: Fixed point theorem in $ M $-fuzzy metric spaces with property (E)..Adv. Fuzzy Math. 1 (2006), 55-56. |
| Reference:
|
[17] Sharma, S.: On fuzzy metric space..Southeast Asian Bull. Math. 26 (2002), 133-145. |
| Reference:
|
[18] Stakgold, I., Hoist, M.: Green’s Functions and Boundary Value Problems..John Wiley and Sons, 2011. |
| Reference:
|
[19] Sun, G., Yang, K.: Generalized fuzzy metric spaces with properties..Res. J. Appl. Sci. Engrg. Technol. 7 (2010), 673-678. |
| Reference:
|
[20] Turkoglua, D., Sangurlu, M.: Fixed point theorems for fuzzy $ \psi $-contractive mappings in fuzzy metric space..J. Intell. Fuzzy Syst. 26 (2014), 137-142. |
| Reference:
|
[21] Zadeh, L. A.: Fuzzy sets..Inform. Control 8 (1965), 338-353. Zbl 0942.00007, |
| . |
