On the convergence of hybrid projection algorithms for asymptotically quasi-ϕϕ-nonexpansive mappings

Using the Mann iteration in an infinite-dimensional Hilbert space, only weak convergence theorems are obtained even for nonexpansive mappings. The purpose of this paper is to modify the Mann iteration and prove the strong convergence theorems without any compactness assumption for asymptotically quasi-ϕϕ-nonexpansive mappings. Moreover, strong convergence theorems are also established in a uniformly smooth and strictly convex Banach space with the Kadec–Klee property.