Relation-Theoretic Banach Contraction Principle in Topological Spaces with an Application
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866908537318277120 |
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| author | Hasanuzzaman, Md Das, Abhishikta Som, Sumit |
| author_facet | Hasanuzzaman, Md Das, Abhishikta Som, Sumit |
| contents | In this article, we extend several relation-theoretic notions to topological spaces. We introduce relation preserving contraction mapping into topological spaces and utilize the same to extend Banach contraction principle in topological spaces employing a binary relation. To illustrate the validity of our main result, we provide a concrete example along with a MATLAB-based visualization of the convergence behavior. Furthermore, we demonstrated the applicability of our main result by finding a solution for a fractional differential equation under some suitable assumptions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_10497 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Relation-Theoretic Banach Contraction Principle in Topological Spaces with an Application Hasanuzzaman, Md Das, Abhishikta Som, Sumit General Mathematics 47H10, 54H25 In this article, we extend several relation-theoretic notions to topological spaces. We introduce relation preserving contraction mapping into topological spaces and utilize the same to extend Banach contraction principle in topological spaces employing a binary relation. To illustrate the validity of our main result, we provide a concrete example along with a MATLAB-based visualization of the convergence behavior. Furthermore, we demonstrated the applicability of our main result by finding a solution for a fractional differential equation under some suitable assumptions. |
| title | Relation-Theoretic Banach Contraction Principle in Topological Spaces with an Application |
| topic | General Mathematics 47H10, 54H25 |
| url | https://arxiv.org/abs/2509.10497 |