In this paper‎, ‎strong convergence theorems of Ishikawa type implicit iteration‎ ‎process with errors for a finite family of asymptotically‎ ‎nonexpansive in the intermediate sense and asymptotically‎ ‎quasi-pseudocontractive type mappings in normed linear spaces are‎ ‎established by using a new analytical method‎, ‎which essentially‎ ‎improve and extend some recent results obtained by Yang‎ ‎...

It is shown that every asymptotically regular or λ-firmly nonexpansive mapping T : C → C has a fixed point whenever C is a finite union of nonempty weakly compact convex subsets of a Banach spaceX which is uniformly convex in every direction. Furthermore, if {Ti}i∈I is any compatible family of strongly nonexpansive self-mappings on such a C and the graphs of Ti, i∈ I, have a nonempty intersecti...

where {an} is a sequence in [0,1] and {un} a sequence in E satisfying ∑∞ n=1‖un‖<∞, is known as Mann iterative scheme with errors. In 1999, Huang [2] studied the above schemes for asymptotically nonexpansive mappings. Recall that a mapping T : C → C is asymptotically nonexpansive if there is a sequence {kn} ⊂ [1,∞) with limn→∞kn = 1 and ‖Tnx−Tny‖ ≤ kn‖x−y‖ for all x,y ∈ C and for all n∈N, where...

in this paper‎, ‎strong convergence theorems of ishikawa type implicit iteration‎ ‎process with errors for a finite family of asymptotically‎ ‎nonexpansive in the intermediate sense and asymptotically‎ ‎quasi-pseudocontractive type mappings in normed linear spaces are‎ ‎established by using a new analytical method‎, ‎which essentially‎ ‎improve and extend some recent results obtained by yang‎ ‎...