Petrov type extension for multivalued contraction mappings
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866916009212903424 |
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| author | Sahin, Hakan Aslantas, Mustafa ALtun, Ishak |
| author_facet | Sahin, Hakan Aslantas, Mustafa ALtun, Ishak |
| contents | In this paper, we introduce the concept of multivalued $λ$% -contracting perimeters of triangles. This concept generalizes the Nadler's contraction by considering triplets of points instead of pairs. Fundamental properties of such mappings are analyzed, including their continuity and their relationship to classical multivalued contractions. By means of a counterexample, we show that a mapping which satisfies the condition of multivalued $λ$-contracting perimeters of triangles is not necessarily a multivalued $λ$-contraction. We also introduce the notion of property of forming a triangle. Then, we investigate the relation between this property and the fact that there is no periodic point of prime period $2$ for any multivalued mapping. Furthermore, using the new concept and property mentioned above, we present some fixed point results for multivalued mappings. Finally, we provide an illustrative and comparative example. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_13358 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Petrov type extension for multivalued contraction mappings Sahin, Hakan Aslantas, Mustafa ALtun, Ishak Functional Analysis 54H25, 47H10 In this paper, we introduce the concept of multivalued $λ$% -contracting perimeters of triangles. This concept generalizes the Nadler's contraction by considering triplets of points instead of pairs. Fundamental properties of such mappings are analyzed, including their continuity and their relationship to classical multivalued contractions. By means of a counterexample, we show that a mapping which satisfies the condition of multivalued $λ$-contracting perimeters of triangles is not necessarily a multivalued $λ$-contraction. We also introduce the notion of property of forming a triangle. Then, we investigate the relation between this property and the fact that there is no periodic point of prime period $2$ for any multivalued mapping. Furthermore, using the new concept and property mentioned above, we present some fixed point results for multivalued mappings. Finally, we provide an illustrative and comparative example. |
| title | Petrov type extension for multivalued contraction mappings |
| topic | Functional Analysis 54H25, 47H10 |
| url | https://arxiv.org/abs/2605.13358 |