Fixed point results and the Ekeland variational principle in vector $B$-metric spaces
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909493039726592 |
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| author | Precup, Radu Stan, Andrei |
| author_facet | Precup, Radu Stan, Andrei |
| contents | In this paper, we extend the concept of \( b \)-metric spaces to the vectorial case, where the distance is vector-valued, and the constant in the triangle inequality axiom is replaced by a matrix. For such spaces, we establish results analogous to those in the \( b \)-metric setting: fixed-point theorems, stability results, and a variant of Ekeland's variational principle. As a consequence, we also derive a variant of Caristi's fixed-point theorem |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_09634 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Fixed point results and the Ekeland variational principle in vector $B$-metric spaces Precup, Radu Stan, Andrei Functional Analysis In this paper, we extend the concept of \( b \)-metric spaces to the vectorial case, where the distance is vector-valued, and the constant in the triangle inequality axiom is replaced by a matrix. For such spaces, we establish results analogous to those in the \( b \)-metric setting: fixed-point theorems, stability results, and a variant of Ekeland's variational principle. As a consequence, we also derive a variant of Caristi's fixed-point theorem |
| title | Fixed point results and the Ekeland variational principle in vector $B$-metric spaces |
| topic | Functional Analysis |
| url | https://arxiv.org/abs/2502.09634 |