We prove that a Banach space X has normal structure provided it contains a finite codimensional subspace Y such that all spreading models for Y have normal structure. We show that a Banach space X is strictly convex if the set of fixed points of any nonexpansive map defined in any convex subset C C X is convex and give a sufficient condition for uniform convexity of a space in terms of nonexpan...

In this paper, we present some common fixed point theorems for two generalized nonexpansive multivalued mappings in CAT(0) spaces as well as in UCED Banach spaces. Moreover, we prove the existence of fixed points for generalized nonexpansive multivalued mappings in complete geodesic metric spaces with convex metric for which the asymptotic center of a bounded sequence in a bounded closed convex...

It is shown that the set of fixed points of a nonexpansive operator is either empty or closed and convex. Under rather general conditions this shows that the minimum norm solution of an operator equation of the form x = Tx exists and is unique, provided that T is nonexpansive. This holds in any strictly convex Banach space, a class of spaces that includes Hilbert spaces as particular case, and ...

Tae-Hwa Kim and Hong-Kun Xu [Strong convergence of modified Mann iterations for asymptotically nonexpansive mappings and semigroups, Nonlinear Analysis 64(2006)1140-1152 ] proved the strong convergence theorems of modified Mann iterations for asymptotically nonexpansive mappings and semigroups on bounded subset C of a Hilbert space by the CQ iteration method. The purpose of this paper is to mod...

The purpose of this paper is to investigate the asymptotic behavior of algorithms for finding solutions for a certain class of variational inequalities V ID(C, I−f) involving nonexpansive type mappings in smooth Banach spaces. We study existence of solutions of variational inequalities V ID(C, I− f) when D is the set of solutions of zeros of accretive operators or the set of fixed points of non...

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...

Suppose that K is a nonempty closed convex subset of a real uniformly convex Banach space E , which is also a nonexpansive retract of E with nonexpansive retraction P . Let {Ti : i ∈ I } be N nonself asymptotically nonexpansive mappings from K to E such that F = {x ∈ K : Ti x = x, i ∈ I } 6= φ, where I = {1, 2, . . . , N }. From arbitrary x0 ∈ K , {xn} is defined by xn = P((1− αn)xn−1 + αnTn(PT...

In this paper, we are concerned with the study of a multi-step iterative scheme with errors insolving a finite family of asymptotically quasinonexpansive self-mappings. We approximate the common fixed points of a finite family of asymptotically quasi-nonexpansive self-mappings by convergence of the scheme in a uniformly convex Banach space. Our results extend and improve some recent results, Q....

In this paper, we introduce the iterative method for finding a common element of the set of solutions of a generalized equilibrium problem and the set of fixed points of a nonexpansive mapping in a Hilbert space and then obtain the sequence converges strongly to a common element of two sets. The results extended and improved the corresponding results of Plubtieng and Punpaeng [S. Plubtieng, R. ...

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...