Iterative algorithm for approximating fixed points of multivalued quasinonexpansive mappings in Banach spaces
Abstract Let E be a strictly convex real Banach space and let D ⊆ E $D\subseteq E$ be a nonempty closed convex subset of E. Let T i : D ⟶ P ( D ) $T_{i}: {D}\longrightarrow \mathcal{P}({D})$ , i = 1 , 2 , 3 , … $i=1,2,3,\ldots $ be a countable family of quasinonexpansive multivalued maps that are co...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2022-03-01
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| Series: | Fixed Point Theory and Algorithms for Sciences and Engineering |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13663-022-00718-7 |
| _version_ | 1818138790254870528 |
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| author | Ma’aruf Shehu Minjibir Chimezie Izuazu |
| author_facet | Ma’aruf Shehu Minjibir Chimezie Izuazu |
| author_sort | Ma’aruf Shehu Minjibir |
| collection | DOAJ |
| description | Abstract Let E be a strictly convex real Banach space and let D ⊆ E $D\subseteq E$ be a nonempty closed convex subset of E. Let T i : D ⟶ P ( D ) $T_{i}: {D}\longrightarrow \mathcal{P}({D})$ , i = 1 , 2 , 3 , … $i=1,2,3,\ldots $ be a countable family of quasinonexpansive multivalued maps that are continuous with respect to the Hausdorff metric, P ( D ) $\mathcal{P}(D)$ is the family of proximinal and bounded subsets of D. Supposing that the family has at least one common fixed point, we show that a Krasnoselskii–Mann-type sequence converges strongly to a common fixed point. Our result generalizes and complements some important results for single-valued and multivalued quasinonexpansive maps. |
| first_indexed | 2024-12-11T10:17:47Z |
| format | Article |
| id | doaj.art-75238d78e1a54e33af0f4ce4535d389b |
| institution | Directory Open Access Journal |
| issn | 2730-5422 |
| language | English |
| last_indexed | 2024-12-11T10:17:47Z |
| publishDate | 2022-03-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Fixed Point Theory and Algorithms for Sciences and Engineering |
| spelling | doaj.art-75238d78e1a54e33af0f4ce4535d389b2022-12-22T01:11:34ZengSpringerOpenFixed Point Theory and Algorithms for Sciences and Engineering2730-54222022-03-012022111210.1186/s13663-022-00718-7Iterative algorithm for approximating fixed points of multivalued quasinonexpansive mappings in Banach spacesMa’aruf Shehu Minjibir0Chimezie Izuazu1African University of Science and TechnologyAfrican University of Science and TechnologyAbstract Let E be a strictly convex real Banach space and let D ⊆ E $D\subseteq E$ be a nonempty closed convex subset of E. Let T i : D ⟶ P ( D ) $T_{i}: {D}\longrightarrow \mathcal{P}({D})$ , i = 1 , 2 , 3 , … $i=1,2,3,\ldots $ be a countable family of quasinonexpansive multivalued maps that are continuous with respect to the Hausdorff metric, P ( D ) $\mathcal{P}(D)$ is the family of proximinal and bounded subsets of D. Supposing that the family has at least one common fixed point, we show that a Krasnoselskii–Mann-type sequence converges strongly to a common fixed point. Our result generalizes and complements some important results for single-valued and multivalued quasinonexpansive maps.https://doi.org/10.1186/s13663-022-00718-7Stirctly convex Banach spaceMultivalued quasinonexpansive mapsHausdorff metricCountable family of mapsStrong convergence |
| spellingShingle | Ma’aruf Shehu Minjibir Chimezie Izuazu Iterative algorithm for approximating fixed points of multivalued quasinonexpansive mappings in Banach spaces Fixed Point Theory and Algorithms for Sciences and Engineering Stirctly convex Banach space Multivalued quasinonexpansive maps Hausdorff metric Countable family of maps Strong convergence |
| title | Iterative algorithm for approximating fixed points of multivalued quasinonexpansive mappings in Banach spaces |
| title_full | Iterative algorithm for approximating fixed points of multivalued quasinonexpansive mappings in Banach spaces |
| title_fullStr | Iterative algorithm for approximating fixed points of multivalued quasinonexpansive mappings in Banach spaces |
| title_full_unstemmed | Iterative algorithm for approximating fixed points of multivalued quasinonexpansive mappings in Banach spaces |
| title_short | Iterative algorithm for approximating fixed points of multivalued quasinonexpansive mappings in Banach spaces |
| title_sort | iterative algorithm for approximating fixed points of multivalued quasinonexpansive mappings in banach spaces |
| topic | Stirctly convex Banach space Multivalued quasinonexpansive maps Hausdorff metric Countable family of maps Strong convergence |
| url | https://doi.org/10.1186/s13663-022-00718-7 |
| work_keys_str_mv | AT maarufshehuminjibir iterativealgorithmforapproximatingfixedpointsofmultivaluedquasinonexpansivemappingsinbanachspaces AT chimezieizuazu iterativealgorithmforapproximatingfixedpointsofmultivaluedquasinonexpansivemappingsinbanachspaces |