Krasnoselskii-Mann method for non-self mappings

Abstract

Let H be a Hilbert space and let C be a closed, convex and nonempty subset of H. If T : C → H is a non-self and non-expansive mapping, we can define a map h : C → R by (Formula presented.). Then, for a fixed (Formula presented.) and for (Formula presented.), we define the Krasnoselskii-Mann algorithm (Formula presented.), where (Formula presented.). We will prove both weak and strong convergence results when C is a strictly convex set and T is an inward mapping.