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: Zhang Binbin, Yin Chenhao, Zhou Chang
Format: Article
Language:English
Published: De Gruyter 2025-06-01
Series:Open Mathematics
Subjects:
Online Access:https://doi.org/10.1515/math-2025-0156
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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
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institution DOAJ
issn 2391-5455
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publishDate 2025-06-01
publisher De Gruyter
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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
work_keys_str_mv AT zhangbinbin ageneralizedfixedpointtheoremforsetvaluedmappingsinbmetricspaces
AT yinchenhao ageneralizedfixedpointtheoremforsetvaluedmappingsinbmetricspaces
AT zhouchang ageneralizedfixedpointtheoremforsetvaluedmappingsinbmetricspaces
AT zhangbinbin generalizedfixedpointtheoremforsetvaluedmappingsinbmetricspaces
AT yinchenhao generalizedfixedpointtheoremforsetvaluedmappingsinbmetricspaces
AT zhouchang generalizedfixedpointtheoremforsetvaluedmappingsinbmetricspaces