| Summary: | 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.
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