Multi-valued mappings on Pompeiu-Hausdorff fuzzy b-metric spaces and a common fixed point result
Introduction/purpose: The study of the theory of fuzzy sets was prompted by the presence of uncertainty as an essential part of real-world problems, leading Zadeh to address the problem of indeterminacy. The notion of fuzzy logic was introduced by Zadeh. Unlike traditional logic theory, where an ele...
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University of Defence in Belgrade
2025-01-01
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| Series: | Vojnotehnički Glasnik |
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| author | Noreddine Makran Stojan N. Radenović |
| author_facet | Noreddine Makran Stojan N. Radenović |
| author_sort | Noreddine Makran |
| collection | DOAJ |
| description | Introduction/purpose: The study of the theory of fuzzy sets was prompted by the presence of uncertainty as an essential part of real-world problems, leading Zadeh to address the problem of indeterminacy. The notion of fuzzy logic was introduced by Zadeh. Unlike traditional logic theory, where an element either belongs to the set or does not, in fuzzy logic, the affiliation of the element to the set is expressed as a number from the interval [0, 1]. Methods: The theory of a fixed point in fuzzy metric spaces can be viewed in different ways, one of which involves the use of fuzzy logic. Fuzzy metric spaces, which are specific types of topological spaces with pleasing "geometric" characteristics, possess a number of appealing properties and are commonly used in both pure and applied sciences. Metric spaces and their various generalizations frequently occur in computer science applications. For this reason, a new space called a Pompeiu-Hausdorff fuzzy b-metric space is constructed in this paper. Results: In this space, some new fixed point results are also formulated and proven. Additionally, a general common fixed point theorem for a pair of multi-valued mappings in Pompeiu-Hausdorff fuzzy b-metric spaces is investigated. The findings obtained in fuzzy metric spaces, such as those discussed in the article of Shen, Y. et al. (2012. Fixed point theorems in fuzzy metric spaces. Applied Mathematics Letters, 25, pp.138-141), are generalized by the results in this paper, and additional specific findings are produced and supported by examples. Conclusion: The study of denotational semantics and their applications in control theory using fuzzy b-metric spaces and Pompeiu-Hausdorff fuzzy b-metric spaces will be an important next step. |
| format | Article |
| id | doaj-art-60fd09816f4b4e2b80f105ad5893acf5 |
| institution | Kabale University |
| issn | 0042-8469 2217-4753 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | University of Defence in Belgrade |
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| series | Vojnotehnički Glasnik |
| spelling | doaj-art-60fd09816f4b4e2b80f105ad5893acf52025-02-10T08:12:01ZengUniversity of Defence in BelgradeVojnotehnički Glasnik0042-84692217-47532025-01-0173112310.5937/vojtehg73-51489Multi-valued mappings on Pompeiu-Hausdorff fuzzy b-metric spaces and a common fixed point resultNoreddine Makran0https://orcid.org/0000-0001-8131-6733Stojan N. Radenović1https://orcid.org/0000-0001-8254-6688University Mohammed Premier, Faculty of Sciences, Department of Mathematics, Oujda, Kingdom of MoroccoUniversity of Belgrade, Faculty of Mechanical Engineering, Belgrade, Republic of SerbiaIntroduction/purpose: The study of the theory of fuzzy sets was prompted by the presence of uncertainty as an essential part of real-world problems, leading Zadeh to address the problem of indeterminacy. The notion of fuzzy logic was introduced by Zadeh. Unlike traditional logic theory, where an element either belongs to the set or does not, in fuzzy logic, the affiliation of the element to the set is expressed as a number from the interval [0, 1]. Methods: The theory of a fixed point in fuzzy metric spaces can be viewed in different ways, one of which involves the use of fuzzy logic. Fuzzy metric spaces, which are specific types of topological spaces with pleasing "geometric" characteristics, possess a number of appealing properties and are commonly used in both pure and applied sciences. Metric spaces and their various generalizations frequently occur in computer science applications. For this reason, a new space called a Pompeiu-Hausdorff fuzzy b-metric space is constructed in this paper. Results: In this space, some new fixed point results are also formulated and proven. Additionally, a general common fixed point theorem for a pair of multi-valued mappings in Pompeiu-Hausdorff fuzzy b-metric spaces is investigated. The findings obtained in fuzzy metric spaces, such as those discussed in the article of Shen, Y. et al. (2012. Fixed point theorems in fuzzy metric spaces. Applied Mathematics Letters, 25, pp.138-141), are generalized by the results in this paper, and additional specific findings are produced and supported by examples. Conclusion: The study of denotational semantics and their applications in control theory using fuzzy b-metric spaces and Pompeiu-Hausdorff fuzzy b-metric spaces will be an important next step.https://scindeks.ceon.rs/article.aspx?artid=0042-84692501001Mfuzzy metric spacefuzzy b-metric spacet-normfixed pointimplicit relation |
| spellingShingle | Noreddine Makran Stojan N. Radenović Multi-valued mappings on Pompeiu-Hausdorff fuzzy b-metric spaces and a common fixed point result Vojnotehnički Glasnik fuzzy metric space fuzzy b-metric space t-norm fixed point implicit relation |
| title | Multi-valued mappings on Pompeiu-Hausdorff fuzzy b-metric spaces and a common fixed point result |
| title_full | Multi-valued mappings on Pompeiu-Hausdorff fuzzy b-metric spaces and a common fixed point result |
| title_fullStr | Multi-valued mappings on Pompeiu-Hausdorff fuzzy b-metric spaces and a common fixed point result |
| title_full_unstemmed | Multi-valued mappings on Pompeiu-Hausdorff fuzzy b-metric spaces and a common fixed point result |
| title_short | Multi-valued mappings on Pompeiu-Hausdorff fuzzy b-metric spaces and a common fixed point result |
| title_sort | multi valued mappings on pompeiu hausdorff fuzzy b metric spaces and a common fixed point result |
| topic | fuzzy metric space fuzzy b-metric space t-norm fixed point implicit relation |
| url | https://scindeks.ceon.rs/article.aspx?artid=0042-84692501001M |
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