Construction of Fixed Points for Asymptotically Nonexpansive Mappings

Fixed points for total asymptotically nonexpansive mappings in a new version of bead ‎space‎

The notion of a bead metric space is defined as a nice generalization of the uniformly convex normed space such as $CAT(0)$ space, where the curvature is bounded from above by zero. In fact, the bead spaces themselves can be considered in particular as natural extensions of convex sets in uniformly convex spaces and normed bead spaces are identical with uniformly convex spaces. In this paper, w...

common fixed points of jointly asymptotically nonexpansive mappings

a definition of two jointly asymptotically nonexpansive mappings s and t on uniformly convex banach space e is studied to approximate common fixed points of two such mappings through weak and strong convergence of an ishikawa type iteration scheme generated by s and t on a bounded closed and convex subset of e. as a consequence of the notion of two jointly asymptotically nonexpansive maps, we c...

Fixed Points of Asymptotically Regular Nonexpansive Mappings on Nonconvex Sets

It is shown that if X is a Banach space and C is a union of finitely many nonempty, pairwise disjoint, closed, and connected subsets {Ci : 1≤ i≤ n} of X , and each Ci has the fixed-point property (FPP) for asymptotically regular nonexpansive mappings, then any asymptotically regular nonexpansive self-mapping of C has a fixed point. We also generalize the Goebel-Schöneberg theorem to some Banach...

Approximating Fixed Points of Total Asymptotically Nonexpansive Mappings

The class of asymptotically nonexpansive maps was introduced by Goebel and Kirk [18] as a generalization of the class of nonexpansive maps. They proved that if K is a nonempty closed convex bounded subset of a real uniformly convex Banach space and T is an asymptotically nonexpansive self-mapping of K , then T has a fixed point. Alber and Guerre-Delabriere have studied in [3–5] weakly contracti...

Approximating fixed points of generalized nonexpansive mappings