for all x, y ∈ K . Let F(T) = {x ∈ K : Tx = x} be denoted as the set of fixed points of a mapping T . The first nonlinear ergodic theorem was proved by Baillon [1] for general nonexpansive mappings in Hilbert space : ifK is a closed and convex subset of and T has a fixed point, then for every x ∈ K , {Tnx} is weakly almost convergent, as n→∞, to a fixed point of T . It was also shown by Pazy [7...

In this paper, we first show that the iteration {xn} defined by xn+1 = P ((1−αn)xn +αnTP [βnTxn + (1− βn)xn]) converges strongly to some fixed point of T when E is a real uniformly convex Banach space and T is a quasi-nonexpansive non-self mapping satisfying Condition A, which generalizes the result due to Shahzad [11]. Next, we show the strong convergence of the Mann iteration process with err...

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 [Convergence the...

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 ‎...

Kohlenbach and Leuştean have shown in 2010 that any asymptotically nonexpansive self-mapping of a bounded nonempty UCW-hyperbolic space has fixed point. In this paper, we adapt construction due to Moloney order provide sequence converges strongly such

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...

and Applied Analysis 3 where J is the duality mapping from E into E∗. It is well known that if C is a nonempty closed convex subset of a Hilbert space H and PC : H → C is the metric projection of H onto C, then PC is nonexpansive. This fact actually characterizes Hilbert spaces and consequently, it is not available in more general Banach spaces. It is obvious from the definition of function φ t...