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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| Format: | Article |
| Language: | English |
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De Gruyter
2025-06-01
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| Series: | Open Mathematics |
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| Online Access: | https://doi.org/10.1515/math-2025-0156 |
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| _version_ | 1849726531264315392 |
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| author | Zhang Binbin Yin Chenhao Zhou Chang |
| author_facet | Zhang Binbin Yin Chenhao Zhou Chang |
| author_sort | Zhang Binbin |
| collection | DOAJ |
| description | 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]. |
| format | Article |
| id | doaj-art-40665279786842e2aba5df976cc5fca4 |
| institution | DOAJ |
| issn | 2391-5455 |
| language | English |
| publishDate | 2025-06-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj-art-40665279786842e2aba5df976cc5fca42025-08-20T03:10:09ZengDe GruyterOpen Mathematics2391-54552025-06-0123113318110.1515/math-2025-0156A generalized fixed-point theorem for set-valued mappings in b-metric spacesZhang Binbin0Yin Chenhao1Zhou Chang2School of Science, Kunming University of Science and Technology, Kunming 650500, P. R. ChinaSchool of Science, Kunming University of Science and Technology, Kunming 650500, P. R. ChinaSchool of Science, Kunming University of Science and Technology, Kunming 650500, P. R. ChinaThe 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].https://doi.org/10.1515/math-2025-0156fixed-pointgeneral graph contractionulam-hyers stabilityb-metric space47h1049j5354h25 |
| spellingShingle | Zhang Binbin Yin Chenhao Zhou Chang A generalized fixed-point theorem for set-valued mappings in b-metric spaces Open Mathematics fixed-point general graph contraction ulam-hyers stability b-metric space 47h10 49j53 54h25 |
| title | A generalized fixed-point theorem for set-valued mappings in b-metric spaces |
| title_full | A generalized fixed-point theorem for set-valued mappings in b-metric spaces |
| title_fullStr | A generalized fixed-point theorem for set-valued mappings in b-metric spaces |
| title_full_unstemmed | A generalized fixed-point theorem for set-valued mappings in b-metric spaces |
| title_short | A generalized fixed-point theorem for set-valued mappings in b-metric spaces |
| title_sort | generalized fixed point theorem for set valued mappings in b metric spaces |
| topic | fixed-point general graph contraction ulam-hyers stability b-metric space 47h10 49j53 54h25 |
| url | https://doi.org/10.1515/math-2025-0156 |
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