‎Fuzzy Metric Spaces and Corresponding Fixed Point Theorems for Fuzzy Type Contraction

Musa Adeku Ibrahim ¹ () Muhammed Raji ² ()
Kamilu Rauf ³ ()

Submited date : 2024-05-06 accepted date : 2024-08-15

Keywords: Fixed point‎, ‎Fuzzy fixed point‎, ‎Contractive type mapping‎, ‎Hausdorff fuzzy metric space‎, Fuzzy mapping‎.,

Abstract :

In this paper‎, ‎we present innovative concepts of fuzzy type contractions and leverage them to establish fixed point theorems for fuzzy mappings within the framework of fuzzy metric spaces‎. ‎The results of this article are applied to multivalued mappings and fuzzy mappings for contractive fuzzy type mappings‎. ‎Through illustrative examples‎, ‎we showcase the practical applicability of our proposed notions and results‎, ‎demonstrating their effectiveness in real-world scenarios‎.

References:

[1] Azam A. Fuzzy fixed points of fuzzy mappings via a rational inequality. Hacettepe Journal of Mathematics and Statistics. 2011; 40(3): 421-431.
[2] Banach S. Sur les operations dans les ensembles abstraits et leur application aux equations itegrales. Fundamenta mathematicae. 1922; 3(1): 133-181. DOI: https://doi.org/10.4064/fm-3-1-133-181
[3] Boriceanu M. Strict fixed point theorems for multivalued operators in b-metric spaces. International Journal of Modern Mathematical Sciences. 2009; 4(3): 285-301.
[4] Butnariu D. Fixed point for fuzzy mapping.Fuzzy Sets and Systems. 1982; 7(2): 191-207. DOI: https://doi.org/10.1016/0165-0114(82)90049-5
[5] Ciri´c LB. A generalization of Banachs contraction principle. Proceedings of the American Mathematical Society. 1974; 45(2): 267-273. DOI: https://doi.org/10.2307/2040075
[6] Czerwik S. Contractive mappings in b-metric spaces. Acta Mathematica et Informatica Universitatis Ostraviensis. 1993; 1(1): 5-11.
[7] Heilpern S. Fuzzy mappings and fixed point theorem. Journal of Mathematical Analysis and Applications. 1981; 83(2): 566-569, DOI: https://doi.org/10.1016/0022-247X(81)90141-4
[8] Hitzler P, Seda AK. Dislocated topologies. Journal of Electrical Engineering. 2000; 51(12): 3-7.
[9] Hussain A, Ishtiaq U, Sulami HA. Fixed point results in fuzzy strong controlled metric spaces with an application to the domain words. Advances in Mathematical Physics. 2023; 1: 4350504, DOI: https://doi.org/10.1155/2023/4350504
[10] Hussain N, Roshan JR, Paravench V, Abbas M. Common fixed point results for weak contractive mappings in ordered dislocated b-metric space with applications. Journal of Inequalities and Applications. 2013; 486: 1-21. DOI: https://doi.org/10.1186/1029-242X-2013-486
[11] Hussain A, Sulami HA, Ishtiaq U. Some new aspects in the intuitionistic fuzzy and neutrosophic fixed point theory. Journal of Function Spaces. 2022; 1: 3138740. DOI: https://doi.org/10.1155/2022/3138740
[12] Ishtiaq U, Hussain A, Sulami HA. Certain new aspects in fuzzy fixed point theory. AIMS Mathematics. 2022; 7(5): 8558-8573. DOI: https://doi.org/10.3934/math.2022477
[13] Kanwal S, Ali A, Al Mazrooei A, Garcia GS. Existence of fuzzy fixed points of set-valued fuzzy mappings in metric and fuzzy metric spaces. AIMS Mathematics. 2023; 8(5): 10095-10112. https://doi.org/10.3934/math.2023511
[14] Kanwal S, Azam A, Shami FA. On coincidence theorem in intuitionistic fuzzy b-metric spaces with application. Journal of Function Spaces. 2022; 1: 5616824. DOI: https://doi.org/10.1155/2022/5616824
[15] Nadler BS. Multivalued contraction mappings. Pacific Journal of Mathematics. 1969; 30(2): 475-488. DOI: https://doi.org/10.2140/pjm.1969.30.475
[16] Phiangsungnoen S, Kumam P. Fuzzy fixed point theorems for multivalued fuzzy contractions in bmetric spaces. Journal of Nonlinear Sciences and Applications (JNSA). 2015; 8(1): 55-63. DOI: http://dx.doi.org/10.22436/jnsa.008.01.07
[17] Phiangsungnoen S, Sintunavarat W, Kumam P. Common α-fuzzy fixed point theorems for fuzzy mappings via βF-admissible pair. Journal of Intelligent &Fuzzy Systems. 2014; 27(5): 2463-2472. DOI: https://doi.org/10.1186/s40467-014-0020-6
[18] Raji M, Ibrahim MA. Fixed point theorems for fuzzy contractions mappings in a dislocated bmetric spaces with applications. Annals of Mathematics and Computer Science. 2024; 21: 1-13. DOI: https://doi.org/10.56947/amcs.v21.233
[19] Raji M, Ibrahim MA, Rauf K, Kehinde R. Common fixed point results for fuzzy F-contractive mappings in a dislocated metric spaces with application. Qeios, (2024), 7, 1-21; DOI:
https://doi.org/10.32388/SV98CN
[20] Rasham T, Kutbi MA, Hussain A, Chandok S. Fuzzy dominated nonlinear operators with applications. Journal of Intelligent & Fuzzy Systems. 2024; 1-15. https://content.iospress.com/articles/journalof-intelligent-and-fuzzy-systems/ifs238250
[21] Rasham T, Saeed F, Agarwal RP, Hussain A, Felhi A. Symmetrical hybrid coupled fuzzy fixed-point results on closed ball in fuzzy metric space with applications. Symmetry. 2023; 15(1): 30. DOI: https://doi.org/10.3390/sym15010030
[22] Rashid M, Shahzad A, Azam A. Fixed point theorems for L-fuzzy mappings in quasi-pseudo metric spaces. Journal of Intelligent & Fuzzy Systems. 2017; 32(1): 499-507. DOI: http://doi.org/10.3233/JIFS152261
[23] Shahzad A, Shoaib A, Khammahawong K, Kumam P. New Ciric type rational fuzzy F-contraction for common fixed points. In: Beyond Traditional Probabilistic Methods in Economics 2. Springer International Publishing; 2019. 215-229. DOI: https://doi.org/10.1007/978-3-030-04200-417
[24] Shahzad A, Shoaib A, Mahmood Q. Fixed point theorems for fuzzy mappings in b- metric space. Italian Journal of Pure and Applied Mathematics. 2017; 38: 419-427.
[25] Shoaib A, Kumam P, Shahzad A, Phiangsungnoen S, Mahmood Q. Fixed point results for fuzzy mappings in a b-metric space. Fixed Point Theory and Applications. 2018; 2: 1-12. DOI: https://doi.org/10.1186/s13663-017-0626-8
[26] Weiss MD. Fixed points and induced fuzzy topologies for fuzzy sets. Journal of Mathematical Analysis and Applications. 1975; 50(1): 142-150. DOI: https://doi.org/10.1016/0022-247X(75)90044-X
[27] Zadeh LA. Fuzzy sets. Information and Control. 1965; 8(3): 338-353. DOI: https://doi.org/10.1016/S0019-9958(65)90241-X