Iterative algorithm for approximating fixed points of multivalued quasinonexpansive mappings in Banach spaces - Minjibir, Ma’aruf Shehu; Izuazu, Chimezie (Fixed point theory and algorithms for sciences and engineering, 2022)
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.