Approximating common fixed points of total asymptotically nonexpansive mappings in CAT(0) spaces

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

Approximating fixed points of asymptotically nonexpansive mappings in Banach spaces by metric projections

for all x, y ∈ C and each n ≥ 1. The class of asymptotically nonexpansive mappings was introduced by Goebel and Kirk [1] as an important generalization of nonexpansive mappings. It was proved in [1] that if C is a nonempty bounded closed convex subset of a real uniformly convex Banach space and T is an asymptotically nonexpansive self mapping on C, then F (T ) is nonempty closed convex subset o...

Approximating Fixed Points of Non-self Asymptotically Nonexpansive Mappings in Banach Spaces

Suppose K is a nonempty closed convex nonexpansive retract of a real uniformly convex Banach space E with P as a nonexpansive retraction. Let T : K → E be an asymptotically nonexpansive mapping with {kn} ⊂ [1,∞) such that ∑∞ n=1(kn − 1) <∞ and F(T) is nonempty, where F(T) denotes the fixed points set of T . Let {αn}, {α′n}, and {α′′ n } be real sequences in (0,1) and ≤ αn,α′n,α′′ n ≤ 1− for all...

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...