On Multivalued Fuzzy Contractions in Extended b-Metric Spaces
In this paper, we establish a Hausdorff metric over the family of nonempty closed subsets of an extended b-metric space. Thereafter, we introduce the concept of multivalued fuzzy contraction mappings and prove related α-fuzzy fixed point theorems in the context of extended b-metric spaces that gener...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Journal of Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2021/5579991 |
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| _version_ | 1832566027016208384 |
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| author | Nayab Alamgir Quanita Kiran Hassen Aydi Yaé Ulrich Gaba |
| author_facet | Nayab Alamgir Quanita Kiran Hassen Aydi Yaé Ulrich Gaba |
| author_sort | Nayab Alamgir |
| collection | DOAJ |
| description | In this paper, we establish a Hausdorff metric over the family of nonempty closed subsets of an extended b-metric space. Thereafter, we introduce the concept of multivalued fuzzy contraction mappings and prove related α-fuzzy fixed point theorems in the context of extended b-metric spaces that generalize Nadler’s fixed point theorem as well as many preexisting results in the literature. Further, we establish α-fuzzy fixed point theorems for Ćirić type fuzzy contraction mappings as a generalization of previous results. Moreover, we give some examples to support the obtained results. |
| format | Article |
| id | doaj-art-d925535f17464f1cbab0214321500bc0 |
| institution | Kabale University |
| issn | 2314-4629 2314-4785 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Mathematics |
| spelling | doaj-art-d925535f17464f1cbab0214321500bc02025-02-03T01:05:27ZengWileyJournal of Mathematics2314-46292314-47852021-01-01202110.1155/2021/55799915579991On Multivalued Fuzzy Contractions in Extended b-Metric SpacesNayab Alamgir0Quanita Kiran1Hassen Aydi2Yaé Ulrich Gaba3School of Natural Sciences, National University of Sciences and Technology (NUST), Sector H-12, Islamabad, PakistanSchool of Electrical Engineering and Computer Science (SEECS), National University of Sciences and Technology (NUST), Sector H-12, Islamabad, PakistanUniversité de Sousse, Institut Supérieur d’Informatique et des Techniques de Communication, H. Sousse 4000, TunisiaDepartment of Mathematics and Applied Mathematics, Sefako Makgatho Health Sciences University, Ga-Rankuwa, South AfricaIn this paper, we establish a Hausdorff metric over the family of nonempty closed subsets of an extended b-metric space. Thereafter, we introduce the concept of multivalued fuzzy contraction mappings and prove related α-fuzzy fixed point theorems in the context of extended b-metric spaces that generalize Nadler’s fixed point theorem as well as many preexisting results in the literature. Further, we establish α-fuzzy fixed point theorems for Ćirić type fuzzy contraction mappings as a generalization of previous results. Moreover, we give some examples to support the obtained results.http://dx.doi.org/10.1155/2021/5579991 |
| spellingShingle | Nayab Alamgir Quanita Kiran Hassen Aydi Yaé Ulrich Gaba On Multivalued Fuzzy Contractions in Extended b-Metric Spaces Journal of Mathematics |
| title | On Multivalued Fuzzy Contractions in Extended b-Metric Spaces |
| title_full | On Multivalued Fuzzy Contractions in Extended b-Metric Spaces |
| title_fullStr | On Multivalued Fuzzy Contractions in Extended b-Metric Spaces |
| title_full_unstemmed | On Multivalued Fuzzy Contractions in Extended b-Metric Spaces |
| title_short | On Multivalued Fuzzy Contractions in Extended b-Metric Spaces |
| title_sort | on multivalued fuzzy contractions in extended b metric spaces |
| url | http://dx.doi.org/10.1155/2021/5579991 |
| work_keys_str_mv | AT nayabalamgir onmultivaluedfuzzycontractionsinextendedbmetricspaces AT quanitakiran onmultivaluedfuzzycontractionsinextendedbmetricspaces AT hassenaydi onmultivaluedfuzzycontractionsinextendedbmetricspaces AT yaeulrichgaba onmultivaluedfuzzycontractionsinextendedbmetricspaces |