On a common fixed point theorem in vector-valued b-metric spaces: Its consequences and application
We introduce a Ćirić type contraction principle in a vector-valued $ b $-metric space that generalizes Perov's contraction principle. We investigate the possible conditions on the mappings $ W, E:G\rightarrow G $ ($ G $ is a non-empty set), for which these mappings admit a unique common fixed p...
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-09-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20231326?viewType=HTML |
| _version_ | 1827807473371709440 |
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| author | Muhammad Nazam Aftab Hussain Asim Asiri |
| author_facet | Muhammad Nazam Aftab Hussain Asim Asiri |
| author_sort | Muhammad Nazam |
| collection | DOAJ |
| description | We introduce a Ćirić type contraction principle in a vector-valued $ b $-metric space that generalizes Perov's contraction principle. We investigate the possible conditions on the mappings $ W, E:G\rightarrow G $ ($ G $ is a non-empty set), for which these mappings admit a unique common fixed point in $ G $ subject to a nonlinear operator $ {\bf F}:\mathbb{P}^{m} \rightarrow \mathbb{R}^{m} $. We illustrate the hypothesis of our findings with examples. We consider an infectious disease model represented by the system of delay integro-differential equations and apply the obtained fixed point theorem to show the existence of a solution to this model. |
| first_indexed | 2024-03-11T21:57:54Z |
| format | Article |
| id | doaj.art-a1df11c0043c4c6aba90199b1df0c522 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-03-11T21:57:54Z |
| publishDate | 2023-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-a1df11c0043c4c6aba90199b1df0c5222023-09-26T01:49:55ZengAIMS PressAIMS Mathematics2473-69882023-09-01811260212604410.3934/math.20231326On a common fixed point theorem in vector-valued b-metric spaces: Its consequences and applicationMuhammad Nazam0Aftab Hussain1Asim Asiri21. Department of Mathematics, Allama Iqbal Open University, H-8, Islamabad 44000, Pakistan2. Department of Mathematics, King Abdulaziz University, Jeddah, 21589, Saudi Arabia2. Department of Mathematics, King Abdulaziz University, Jeddah, 21589, Saudi ArabiaWe introduce a Ćirić type contraction principle in a vector-valued $ b $-metric space that generalizes Perov's contraction principle. We investigate the possible conditions on the mappings $ W, E:G\rightarrow G $ ($ G $ is a non-empty set), for which these mappings admit a unique common fixed point in $ G $ subject to a nonlinear operator $ {\bf F}:\mathbb{P}^{m} \rightarrow \mathbb{R}^{m} $. We illustrate the hypothesis of our findings with examples. We consider an infectious disease model represented by the system of delay integro-differential equations and apply the obtained fixed point theorem to show the existence of a solution to this model.https://www.aimspress.com/article/doi/10.3934/math.20231326?viewType=HTMLcommon fixed point$ (\zeta{\bf f}) $-Ćirić contraction$ \zeta $-complete vector-valued $ b $-metric space |
| spellingShingle | Muhammad Nazam Aftab Hussain Asim Asiri On a common fixed point theorem in vector-valued b-metric spaces: Its consequences and application AIMS Mathematics common fixed point $ (\zeta {\bf f}) $-Ćirić contraction $ \zeta $-complete vector-valued $ b $-metric space |
| title | On a common fixed point theorem in vector-valued b-metric spaces: Its consequences and application |
| title_full | On a common fixed point theorem in vector-valued b-metric spaces: Its consequences and application |
| title_fullStr | On a common fixed point theorem in vector-valued b-metric spaces: Its consequences and application |
| title_full_unstemmed | On a common fixed point theorem in vector-valued b-metric spaces: Its consequences and application |
| title_short | On a common fixed point theorem in vector-valued b-metric spaces: Its consequences and application |
| title_sort | on a common fixed point theorem in vector valued b metric spaces its consequences and application |
| topic | common fixed point $ (\zeta {\bf f}) $-Ćirić contraction $ \zeta $-complete vector-valued $ b $-metric space |
| url | https://www.aimspress.com/article/doi/10.3934/math.20231326?viewType=HTML |
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