Iterative construction of fixed points of asymptotically nonexpansive mappings

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...

Approximating fixed points of generalized nonexpansive mappings

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...

Iterative Approximation of Common Fixed Points of Two Nonself Asymptotically Nonexpansive Mappings

Suppose that K is nonempty closed convex subset of a uniformly convex and smooth Banach space E with P as a sunny nonexpansive retraction and F : F T1 ∩ F T2 {x ∈ K : T1x T2x x}/ ∅. Let T1, T2 : K → E be two weakly inward nonself asymptotically nonexpansive mappings with respect to P with two sequences {k i n } ⊂ 1,∞ satisfying ∑∞ n 1 k i n − 1 < ∞ i 1, 2 , respectively. For any given x1 ∈ K, s...