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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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Vilnius University Press
2025-02-01
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| Series: | Nonlinear Analysis |
| Subjects: | |
| Online Access: | https://www.zurnalai.vu.lt/nonlinear-analysis/article/view/38968 |
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| Summary: | 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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| ISSN: | 1392-5113 2335-8963 |