A generalized fixed-point theorem for set-valued mappings in b-metric spaces
The aim of this article is to present a local generalized fixed-point theorem for set-valued mappings in b-metric spaces, which brings together the framework of different (such as Nadler’s and Kannan’s) fixed-point theorems. For general set-valued graph contractions, a global fixed-point theorem and...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2025-06-01
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| Series: | Open Mathematics |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/math-2025-0156 |
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| Summary: | The aim of this article is to present a local generalized fixed-point theorem for set-valued mappings in b-metric spaces, which brings together the framework of different (such as Nadler’s and Kannan’s) fixed-point theorems. For general set-valued graph contractions, a global fixed-point theorem and qualitative results concerning the fixed-point sets are obtained. We also provide an answer to the open question regarding Ulam-Hyers stability of the fixed-point inclusion proposed in [Petruşel et al., Multi-valued graph contraction principle with applications, Optimization 69 (2020), 1541–1556]. |
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| ISSN: | 2391-5455 |