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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.13147 |
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| _version_ | 1866917490753273856 |
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| author | Popescu, Ovidiu |
| author_facet | Popescu, Ovidiu |
| contents | In this paper we introduce a corrected extension of Burton's theory of large contractions in the context of triangle-perimeter contractions introduced by Petrov. Combining these two lines of research, we prove a fixed point result for large triangle-perimeter contractions with an auxiliary assumption, which is of utmost importance. Firstly, we give a counterexample to the main result related to large triangle-perimeter contractions that currently exists in literature. Then, we prove that given an additional condition, a fixed point result for large triangle-perimeter contractions holds. Lastly, we illustrate with an example that this new framework is strictly broader than Burton's and Petrov's theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_13147 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On fixed point results in metric spaces for large triangle-perimeter contractions Popescu, Ovidiu Dynamical Systems 47H10, 47H09 In this paper we introduce a corrected extension of Burton's theory of large contractions in the context of triangle-perimeter contractions introduced by Petrov. Combining these two lines of research, we prove a fixed point result for large triangle-perimeter contractions with an auxiliary assumption, which is of utmost importance. Firstly, we give a counterexample to the main result related to large triangle-perimeter contractions that currently exists in literature. Then, we prove that given an additional condition, a fixed point result for large triangle-perimeter contractions holds. Lastly, we illustrate with an example that this new framework is strictly broader than Burton's and Petrov's theory. |
| title | On fixed point results in metric spaces for large triangle-perimeter contractions |
| topic | Dynamical Systems 47H10, 47H09 |
| url | https://arxiv.org/abs/2605.13147 |