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 Dsubseteq E be a nonempty closed convex subset of E. Let T_{i}: {D}longrightarrow mathcal{P}({D}), i=1,2,3,ldots be a countable family of quasinonexpansive multivalued maps that are continuous with respect to the Hausdorff metric, 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.