Strong convergence of a CQ method for k-strictly asymptotically pseudocontractive mappings

Abstract

Let E be a real q-uniformly smooth Banach space, which is also uniformly convex (for example, Lp or ℓp spaces, 1 < p < ∞), and C be a nonempty bounded closed convex subset of E. Let T : C → C be a k-strictly asymptotically pseudocontractive map with a nonempty fixed point set. A hybrid algorithm is constructed to approximate fixed points of such maps. Furthermore, strong convergence of the proposed algorithm is established. © 2012 Dehghan and Shahzad; licensee Springer.