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

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Abstract Let E be a strictly convex real Banach space and let $D\subseteq E$ D ⊆ E be a nonempty closed convex subset of E. Let $T_{i}: {D}\longrightarrow \mathcal{P}({D})$ T i : D ⟶ P ( D ) , $i=1,2,3,\ldots $ i = 1 , 2 , 3 , … be a countable family of quasinonexpansive multivalued maps that are continuous with respect to the Hausdorff metric, $\mathcal{P}(D)$ 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.

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