Fixed point results via fuzzy mappings in b-metric spaces and an application to differential equations
Abstract This paper introduces the concept of ( P , ψ ) $(P,\psi )$ -type almost contractive conditions for fuzzy mappings in b-metric spaces. This novel framework is employed to establish certain fuzzy fixed point results in complete b-metric spaces. An illustrative example is provided to validate...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-05-01
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| Series: | Journal of Inequalities and Applications |
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| Online Access: | https://doi.org/10.1186/s13660-025-03317-3 |
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| _version_ | 1850107684741709824 |
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| author | Usman Shehzad Samina Batul Dur-e-Shehwar Sagheer Irshad Ayoob Nabil Mlaiki |
| author_facet | Usman Shehzad Samina Batul Dur-e-Shehwar Sagheer Irshad Ayoob Nabil Mlaiki |
| author_sort | Usman Shehzad |
| collection | DOAJ |
| description | Abstract This paper introduces the concept of ( P , ψ ) $(P,\psi )$ -type almost contractive conditions for fuzzy mappings in b-metric spaces. This novel framework is employed to establish certain fuzzy fixed point results in complete b-metric spaces. An illustrative example is provided to validate the assumptions of the main theorem, ensuring the existence of fuzzy fixed points. Furthermore, the existence of a solution to a second-order nonlinear boundary value problem is demonstrated by transforming the problem into a fixed point equation and applying the proven results. Several corollaries are derived as consequences of the main findings. The results presented in this work extend and generalize numerous existing fixed point theorems in the literature. |
| format | Article |
| id | doaj-art-4e28bc9b1b5e456e8f90d8232a9b8e51 |
| institution | OA Journals |
| issn | 1029-242X |
| language | English |
| publishDate | 2025-05-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj-art-4e28bc9b1b5e456e8f90d8232a9b8e512025-08-20T02:38:32ZengSpringerOpenJournal of Inequalities and Applications1029-242X2025-05-012025112210.1186/s13660-025-03317-3Fixed point results via fuzzy mappings in b-metric spaces and an application to differential equationsUsman Shehzad0Samina Batul1Dur-e-Shehwar Sagheer2Irshad Ayoob3Nabil Mlaiki4Capital University of Science and TechnologyCapital University of Science and TechnologyCapital University of Science and TechnologyDepartment of Mathematics and Sciences, Prince Sultan UniversityDepartment of Mathematics and Sciences, Prince Sultan UniversityAbstract This paper introduces the concept of ( P , ψ ) $(P,\psi )$ -type almost contractive conditions for fuzzy mappings in b-metric spaces. This novel framework is employed to establish certain fuzzy fixed point results in complete b-metric spaces. An illustrative example is provided to validate the assumptions of the main theorem, ensuring the existence of fuzzy fixed points. Furthermore, the existence of a solution to a second-order nonlinear boundary value problem is demonstrated by transforming the problem into a fixed point equation and applying the proven results. Several corollaries are derived as consequences of the main findings. The results presented in this work extend and generalize numerous existing fixed point theorems in the literature.https://doi.org/10.1186/s13660-025-03317-3Fixed point theory (FPT)Fixed point results (FPR)Banach contraction principle (BCP)b-metric space (BMS)Fuzzy mapping (FM) |
| spellingShingle | Usman Shehzad Samina Batul Dur-e-Shehwar Sagheer Irshad Ayoob Nabil Mlaiki Fixed point results via fuzzy mappings in b-metric spaces and an application to differential equations Journal of Inequalities and Applications Fixed point theory (FPT) Fixed point results (FPR) Banach contraction principle (BCP) b-metric space (BMS) Fuzzy mapping (FM) |
| title | Fixed point results via fuzzy mappings in b-metric spaces and an application to differential equations |
| title_full | Fixed point results via fuzzy mappings in b-metric spaces and an application to differential equations |
| title_fullStr | Fixed point results via fuzzy mappings in b-metric spaces and an application to differential equations |
| title_full_unstemmed | Fixed point results via fuzzy mappings in b-metric spaces and an application to differential equations |
| title_short | Fixed point results via fuzzy mappings in b-metric spaces and an application to differential equations |
| title_sort | fixed point results via fuzzy mappings in b metric spaces and an application to differential equations |
| topic | Fixed point theory (FPT) Fixed point results (FPR) Banach contraction principle (BCP) b-metric space (BMS) Fuzzy mapping (FM) |
| url | https://doi.org/10.1186/s13660-025-03317-3 |
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