Algorithms for Approximating fixed Points of Multivalued Quasi-Nonexpansive Mappings in Banach Spaces

Abstract

Let E be a strictly convex real Banach space and let D ⊆ E be a non-empty closed convex subset of E. Let {T}i∈I be a finite family of quasi-nonexpansive multivalued map which are continuous with respect to the Hausdorff metric, where Ti : D −→ PB(D), for all i ∈ I. Suppose that the family has a least one common fixed point, a Krasnolselskii-Mann-type sequence is shown to converge strongly to a common fixed point of Ti”s. Our result generalizes and complements some important results for single-valued and multivalued quasi-nonexpansive maps. Futhermore, we considered a countable family of quasi-nonexpansive multivalued map and proved a similar result.