| Title:
|
Fixed point result in controlled fuzzy metric spaces with application to dynamic market equilibrium (English) |
| Author:
|
Tiwari, Rakesh |
| Author:
|
Rakočević, Vladimir |
| Author:
|
Rajput, Shraddha |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 (print) |
| ISSN:
|
1805-949X (online) |
| Volume:
|
58 |
| Issue:
|
3 |
| Year:
|
2022 |
| Pages:
|
335-353 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper, we introduce $\Theta_f$-type controlled fuzzy metric spaces and establish some fixed point results in this spaces. We provide suitable examples to validate our result. We also employ an application to substantiate the utility of our established result for finding the unique solution of an integral equation emerging in the dynamic market equilibrium aspects to economics. (English) |
| Keyword:
|
fixed point |
| Keyword:
|
fuzzy metric spaces |
| Keyword:
|
controlled fuzzy metric spaces |
| Keyword:
|
fuzzy $\Theta _f$-contractive mapping |
| Keyword:
|
dynamic market equilibrium |
| MSC:
|
47H10 |
| MSC:
|
54H25 |
| MSC:
|
A11 |
| idZBL:
|
Zbl 07613049 |
| idMR:
|
MR4494095 |
| DOI:
|
10.14736/kyb-2022-3-0335 |
| . |
| Date available:
|
2022-10-06T14:46:06Z |
| Last updated:
|
2023-03-13 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/151034 |
| . |
| Reference:
|
[1] Aydi, H., Bota, M., Karapinar, E., S.Moradi: A common fixed point for weak $\phi$-contractions on $b$-metric spaces..Fixed Point Theory 13 (2012), 337-346. MR 3024322 |
| Reference:
|
[2] Afshari, H., Atapour, M., Aydi, H.: Generalized $\alpha-\psi-$Geraghty multivalued mappings on $b$-metric spaces endowed with a graph..J. Appl. Eng. Math. 7 (2017), 248-260. MR 3741903 |
| Reference:
|
[3] Aydi, H., R.Banković, I.Mitrović, Nazam, M.: Nemytzki-Edelstein-Meir-Keeler type results in b-metric spaces..Discret. Dyn. Nat. Soc. (2018), 4745764. MR 3827845, |
| Reference:
|
[4] Alharbi, N., Aydi, H., Felhi, A., Ozel, C., Sahmim, S.: $\alpha$-Contractive mappings on rectangular b-metric spaces and an application to integral equations..J. Math. Anal. 9 (2018), 47-60. MR 3896745 |
| Reference:
|
[5] Banach, S.: Sur les opérations dans les ensembles abstraits et leur application aux équations intégrals..Fund. Math. 3 (1922), 133-181. MR 3949898, |
| Reference:
|
[6] Bakhtin, I. A.: The contraction mapping principle in almost metric spaces..Funct. Anal. 30 (1989), 26-37. MR 1204890, |
| Reference:
|
[7] Boriceanu, M., Petrusel., A., Rus, I. A.: Fixed point theorems for some multivalued generalized contraction in b-metric spaces..Int. J. Math. Statist. 6 (2010), 65-76. MR 2520394 |
| Reference:
|
[8] Czerwik, S.: Contraction mappings in b-metric spaces..Acta Math. Inform. Univ. Ostrava 1 (1993), 5-11. MR 1250922, |
| Reference:
|
[9] Dowling, T. E.: Introduction to Mathematical Economics..Schaum's Outline Series, 2001. |
| Reference:
|
[10] George, A., Veeramani, P.: On some results in fuzzy metric spaces..Fuzzy Sets Systems 64 (1994), 395-399. Zbl 0843.54014, MR 1289545, |
| Reference:
|
[11] Gopal, D.: Contributions to fixed point theory of fuzzy contractive mappings..Adv. Metric Fixed Point Theory Appl. (2021), 241-282. MR 4306467, |
| Reference:
|
[12] Gopal, D., T.Došenović: Fixed point theory for fuzzy contractive mappings..Metric Struct. Fixed Point Theory (2021), 199-244. MR 4394399, |
| Reference:
|
[13] Gopal, D., Vetro, C.: Some new fixed point theorems in fuzzy metric spaces..Iranian J. Fuzzy Systems 11(2014), 3, 95-107. MR 3237493, |
| Reference:
|
[14] Grabiec, M.: Fixed points in fuzzy metric spaces..Fuzzy Sets Systems 27 (1988), 385-389. Zbl 0664.54032, MR 0956385, |
| Reference:
|
[15] Hao, Y., Guan, H.: On some common fixed point results for weakly contraction mappings with application..J. Funct. Spaces 2021 (2021), 5573983. MR 4243986, |
| Reference:
|
[16] Kim, J. K.: Common fixed point theorems for non-compatible self-mappings in b-fuzzy metric spaces..J. Comput. Anal. Appl. 22 (2017), 336-345. MR 3643679 |
| Reference:
|
[17] Kramosil, I., Michálek, J.: Fuzzy metric and statistical metric spaces..Kybernetika 11 (1975), 326-334. MR 0410633, |
| Reference:
|
[18] Mehmood, F., Ali, R., Ionescu, C., Kamran, T.: Extended fuzzy b-metric spaces..J. Math. Anal. 8 (2017), 124-131. MR 3750093, |
| Reference:
|
[19] Melliani, S., Moussaoui, A.: Fixed point theorem using a new class of fuzzy contractive mappings..J. Univer. Math. 1 (2018), 2, 148-154. |
| Reference:
|
[20] Mihet, D.: Fuzzy $\psi$-contractive mappings in non-archimedean fuzzy metric spaces..Fuzzy Sets Systems 159 (2008), 6, 739-744. MR 2410532, |
| Reference:
|
[21] Mlaiki, N., Aydi, H., Souayah, N., Abdeljawad, T.: Controlled metric type spaces and the related contraction principle..Math. Molecul. Divers. Preservat. Int. 6 (2018), 1-7. |
| Reference:
|
[22] Nadaban, S.: Fuzzy b-metric spaces..Int. J. Comput. Commun. Control 11 (2016), 273-281. |
| Reference:
|
[23] Nasr, H. S., Imdad, M., Khan, I., Hasanuzzaman, M.: Fuzzy $\Theta_f$-contractive mappings and their fixed points with applications..J. Intell. Fuzzy Systems (2020), 1-10. |
| Reference:
|
[24] Sezen, M. S.: Controlled fuzzy metric spaces and some related fixed point results..Numer. Part. Different. Equations (2020), 1-11. MR 4191089, |
| Reference:
|
[25] Shukla, S., Gopal, D., Sintunavarat, W.: A new class of fuzzy contractive mappings and fixed point theorems..Fuzzy Sets Systems 350 (2018), 85-94. MR 3852589, |
| Reference:
|
[26] Schweizer, B., Sklar, A.: Statistical metric spaces..Paciffc J. Math. 10 (1960), 313-334. Zbl 0136.39301, MR 0115153, |
| Reference:
|
[27] Wardowski, D.: Fuzzy contractive mappings and fixed points in fuzzy metric spaces..Fuzzy Sets Systems 222 (2013), 108-114. MR 3053895, |
| Reference:
|
[28] Zadeh, A. L.: Fuzzy sets..Inform. Control 8 (1965), 338-353. Zbl 0942.00007, MR 0219427, |
| . |
