Fixed point results for single and multivalued three-points contractions
In this paper, we are concerned with the study of the existence of fixed points for single and multivalued three-points contractions. Namely, we first introduce a new class of singlevalued mappings defined on a metric space equipped with three metrics. A fixed point theorem is established for such...
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| Format: | Article |
| Language: | English |
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Vilnius University Press
2025-02-01
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| Series: | Nonlinear Analysis |
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| Online Access: | https://www.zurnalai.vu.lt/nonlinear-analysis/article/view/38968 |
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| author | Mohamed Jleli Evgeniy Petrov Bessem Samet |
| author_facet | Mohamed Jleli Evgeniy Petrov Bessem Samet |
| author_sort | Mohamed Jleli |
| collection | DOAJ |
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In this paper, we are concerned with the study of the existence of fixed points for single and multivalued three-points contractions. Namely, we first introduce a new class of singlevalued mappings defined on a metric space equipped with three metrics. A fixed point theorem is established for such mappings. The obtained result recovers that established recently by the second author [E. Petrov, Fixed point theorem for mappings contracting perimeters of triangles, J. Fixed Point Theory Appl., 25(3):74, 2023] for the class of single-valued mappings contracting perimeters of triangles. We next extend our study by introducing the class of multivalued three points contractions. A fixed point theorem, which is a multivalued version of that obtained in the above reference, is established. Some examples showing the validity of our obtained results are provided.
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| format | Article |
| id | doaj-art-fa82faf4e7284eeb8a005bf748b91ccc |
| institution | DOAJ |
| issn | 1392-5113 2335-8963 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | Vilnius University Press |
| record_format | Article |
| series | Nonlinear Analysis |
| spelling | doaj-art-fa82faf4e7284eeb8a005bf748b91ccc2025-08-20T03:05:38ZengVilnius University PressNonlinear Analysis1392-51132335-89632025-02-0130210.15388/namc.2025.30.38968Fixed point results for single and multivalued three-points contractionsMohamed Jleli0Evgeniy Petrov1Bessem Samet2King Saud UniversityInstitute of Applied Mathematics and Mechanics of the NAS of UkraineKing Saud University In this paper, we are concerned with the study of the existence of fixed points for single and multivalued three-points contractions. Namely, we first introduce a new class of singlevalued mappings defined on a metric space equipped with three metrics. A fixed point theorem is established for such mappings. The obtained result recovers that established recently by the second author [E. Petrov, Fixed point theorem for mappings contracting perimeters of triangles, J. Fixed Point Theory Appl., 25(3):74, 2023] for the class of single-valued mappings contracting perimeters of triangles. We next extend our study by introducing the class of multivalued three points contractions. A fixed point theorem, which is a multivalued version of that obtained in the above reference, is established. Some examples showing the validity of our obtained results are provided. https://www.zurnalai.vu.lt/nonlinear-analysis/article/view/38968fixed pointssingle-valued three-points contractionsmultivalued three-points contractionsmappings contracting perimeters of triangles |
| spellingShingle | Mohamed Jleli Evgeniy Petrov Bessem Samet Fixed point results for single and multivalued three-points contractions Nonlinear Analysis fixed points single-valued three-points contractions multivalued three-points contractions mappings contracting perimeters of triangles |
| title | Fixed point results for single and multivalued three-points contractions |
| title_full | Fixed point results for single and multivalued three-points contractions |
| title_fullStr | Fixed point results for single and multivalued three-points contractions |
| title_full_unstemmed | Fixed point results for single and multivalued three-points contractions |
| title_short | Fixed point results for single and multivalued three-points contractions |
| title_sort | fixed point results for single and multivalued three points contractions |
| topic | fixed points single-valued three-points contractions multivalued three-points contractions mappings contracting perimeters of triangles |
| url | https://www.zurnalai.vu.lt/nonlinear-analysis/article/view/38968 |
| work_keys_str_mv | AT mohamedjleli fixedpointresultsforsingleandmultivaluedthreepointscontractions AT evgeniypetrov fixedpointresultsforsingleandmultivaluedthreepointscontractions AT bessemsamet fixedpointresultsforsingleandmultivaluedthreepointscontractions |