Common best proximity point theorems under proximal F ρ ♭ $F_{\rho \flat}$ -weak dominance with application
Abstract In partial ♭-metric spaces, we first define F ρ ♭ $F_{\rho \flat}$ -weak contraction mappings and develop fixed point theorems in these mappings. In the context of ♭-metric and partial ♭-metric spaces, this study aims to establish the concept of proximally F ρ ♭ $F_{\rho \flat}$ -weakly dom...
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| Format: | Article |
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SpringerOpen
2025-08-01
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| Series: | Fixed Point Theory and Algorithms for Sciences and Engineering |
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| Online Access: | https://doi.org/10.1186/s13663-025-00795-4 |
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| author | Asaye Ayele Kidane Koyas |
| author_facet | Asaye Ayele Kidane Koyas |
| author_sort | Asaye Ayele |
| collection | DOAJ |
| description | Abstract In partial ♭-metric spaces, we first define F ρ ♭ $F_{\rho \flat}$ -weak contraction mappings and develop fixed point theorems in these mappings. In the context of ♭-metric and partial ♭-metric spaces, this study aims to establish the concept of proximally F ρ ♭ $F_{\rho \flat}$ -weakly dominated pair of mappings and derive common best proximity point theorems using this pair of mappings. The best proximity point and associated fixed point theorems in the literature are generalized by our new findings. Furthermore, we illustrate our findings with examples. Finally, as evidence for our conclusion, we demonstrate that an integral equation has a solution. |
| format | Article |
| id | doaj-art-7f32d939b19e42d19f6b3b9be49355ee |
| institution | Kabale University |
| issn | 2730-5422 |
| language | English |
| publishDate | 2025-08-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Fixed Point Theory and Algorithms for Sciences and Engineering |
| spelling | doaj-art-7f32d939b19e42d19f6b3b9be49355ee2025-08-20T03:46:16ZengSpringerOpenFixed Point Theory and Algorithms for Sciences and Engineering2730-54222025-08-012025112510.1186/s13663-025-00795-4Common best proximity point theorems under proximal F ρ ♭ $F_{\rho \flat}$ -weak dominance with applicationAsaye Ayele0Kidane Koyas1Department of Mathematics, Jimma UniversityDepartment of Mathematics, Jimma UniversityAbstract In partial ♭-metric spaces, we first define F ρ ♭ $F_{\rho \flat}$ -weak contraction mappings and develop fixed point theorems in these mappings. In the context of ♭-metric and partial ♭-metric spaces, this study aims to establish the concept of proximally F ρ ♭ $F_{\rho \flat}$ -weakly dominated pair of mappings and derive common best proximity point theorems using this pair of mappings. The best proximity point and associated fixed point theorems in the literature are generalized by our new findings. Furthermore, we illustrate our findings with examples. Finally, as evidence for our conclusion, we demonstrate that an integral equation has a solution.https://doi.org/10.1186/s13663-025-00795-4Common best proximity pointProximal F ρ ♭ $F_{\rho \flat}$ -weak dominanceProximally commuteFixed point |
| spellingShingle | Asaye Ayele Kidane Koyas Common best proximity point theorems under proximal F ρ ♭ $F_{\rho \flat}$ -weak dominance with application Fixed Point Theory and Algorithms for Sciences and Engineering Common best proximity point Proximal F ρ ♭ $F_{\rho \flat}$ -weak dominance Proximally commute Fixed point |
| title | Common best proximity point theorems under proximal F ρ ♭ $F_{\rho \flat}$ -weak dominance with application |
| title_full | Common best proximity point theorems under proximal F ρ ♭ $F_{\rho \flat}$ -weak dominance with application |
| title_fullStr | Common best proximity point theorems under proximal F ρ ♭ $F_{\rho \flat}$ -weak dominance with application |
| title_full_unstemmed | Common best proximity point theorems under proximal F ρ ♭ $F_{\rho \flat}$ -weak dominance with application |
| title_short | Common best proximity point theorems under proximal F ρ ♭ $F_{\rho \flat}$ -weak dominance with application |
| title_sort | common best proximity point theorems under proximal f ρ ♭ f rho flat weak dominance with application |
| topic | Common best proximity point Proximal F ρ ♭ $F_{\rho \flat}$ -weak dominance Proximally commute Fixed point |
| url | https://doi.org/10.1186/s13663-025-00795-4 |
| work_keys_str_mv | AT asayeayele commonbestproximitypointtheoremsunderproximalfrfrhoflatweakdominancewithapplication AT kidanekoyas commonbestproximitypointtheoremsunderproximalfrfrhoflatweakdominancewithapplication |