Three point analogue of Ćirić-Reich-Rus type mappings with non-unique fixed points
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912221739614208 |
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| author | Bisht, Ravindra K. Petrov, Evgeniy |
| author_facet | Bisht, Ravindra K. Petrov, Evgeniy |
| contents | In this paper, we introduce a three-point analogue of Ćirić-Reich-Rus type mappings, termed as generalized Ćirić-Reich-Rus type mappings. We demonstrate that these mappings generally exhibit discontinuity within their domain of definition but necessitate continuity at their fixed points. We showcase the existence and non-uniqueness of fixed points for these generalized Ćirić-Reich-Rus type mappings. By imposing additional conditions, specifically asymptotic regularity and continuity, we extend the applicability of fixed-point theorems to a broader class of mappings. Finally, we obtain two fixed point theorems for generalized Ćirić-Reich-Rus type mappings in metric spaces that are not necessarily complete. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_02595 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Three point analogue of Ćirić-Reich-Rus type mappings with non-unique fixed points Bisht, Ravindra K. Petrov, Evgeniy General Topology Primary 47H10, Secondary 47H09 In this paper, we introduce a three-point analogue of Ćirić-Reich-Rus type mappings, termed as generalized Ćirić-Reich-Rus type mappings. We demonstrate that these mappings generally exhibit discontinuity within their domain of definition but necessitate continuity at their fixed points. We showcase the existence and non-uniqueness of fixed points for these generalized Ćirić-Reich-Rus type mappings. By imposing additional conditions, specifically asymptotic regularity and continuity, we extend the applicability of fixed-point theorems to a broader class of mappings. Finally, we obtain two fixed point theorems for generalized Ćirić-Reich-Rus type mappings in metric spaces that are not necessarily complete. |
| title | Three point analogue of Ćirić-Reich-Rus type mappings with non-unique fixed points |
| topic | General Topology Primary 47H10, Secondary 47H09 |
| url | https://arxiv.org/abs/2502.02595 |