Iterative algorithm for approximating fixed points of multivalued quasinonexpansive mappings in Banach spaces

Let E be a strictly convex real Banach space and let D ⊆ E be a nonempty closed convex subset of E . Let T i : D ⟶ P ( D ) , i = 1 , 2 , 3 , … be a countable family of quasinonexpansive multivalued maps that are continuous with respect to the Hausdorff metric, P ( D ) is the family of proximinal and...

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Bibliographic Details
Published in:Fixed point theory and algorithms for sciences and engineering Vol. 2022; no. 1; pp. 1 - 12
Main Authors: Minjibir, Ma’aruf Shehu, Izuazu, Chimezie
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 07.03.2022
SpringerOpen
Subjects:
Analysis
Applications of Mathematics
Countable family of maps
Differential Geometry
Hausdorff metric
Mathematical and Computational Biology
Mathematics
Mathematics and Statistics
Multivalued quasinonexpansive maps
Stirctly convex Banach space
Strong convergence
Topology
Strong convergence
47H10
Countable family of maps
Multivalued quasinonexpansive maps
47H09
47J25
Stirctly convex Banach space
Hausdorff metric
ISSN:2730-5422, 2730-5422
Online Access:Get full text
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Summary:Let E be a strictly convex real Banach space and let D ⊆ E be a nonempty closed convex subset of E . Let T i : D ⟶ P ( D ) , i = 1 , 2 , 3 , … be a countable family of quasinonexpansive multivalued maps that are continuous with respect to the Hausdorff metric, 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.
ISSN:2730-5422
2730-5422
DOI:10.1186/s13663-022-00718-7