A RANDOM FIXED POINT ITERATION FOR THREE RANDOM OPERATORS ON UNIFORMLY CONVEX BANACH SPACES

In the present paper we introduce a random iteration scheme for three random operators defined on a closed and convex subset of a uniformly convex Banach space and prove its convergence to a common fixed point of three random operators. The result is also an extension of a known theorem in the corresponding non-random case.

STRONG CONVERGENCE OF APPROXIMATED SEQUENCES FOR NONEXPANSIVE MAPPINGS IN BANACH SPACES

This paper studies the convergence of the sequence defined by x0 ∈ C, xn＋l =αnu＋（1-αn）Txn, n=0, 1,2,..., where 0 ≤αn ≤ 1, limn→∞ αn = 0, ∑n=0^∞ αn = ∞, and T is a nonexpansive mapping from a nonempty closed convex subset C of a Banach space X into itself. The iterative sequence {xn} converges strongly to a fixed point of T in the case when X is a uniformly convex Banach space with a uniformly Gateaux differentiable norm or a uniformly smooth Banach space only. The results presented in this paper extend and improve some recent results.

ON THE EXISTENCE OF COMMON FIXED POINTS FOR A PAIR OF LIPSCHITZIAN MAPPINGS IN BANACH SPACES

The existence of common fixed points for a pair of Lipschitzian mappings in Banach spaces is proved. By using this result, some common fixed point theorems are also established for these mappings in Hilbert spaces, in L p spaces, in Hardy spaces H p, and in Sobolev spaces H r,p , for 1<p<+∞ and r≥0.

Property A_(UB) of Metric Spaces under Decompositions of Finite Depth

Property AUB is the notion in metric geometry which has applications in higher index problems.In this paper,the permanence property of property AUB of metric spaces under large scale decompositions of finite depth is proved.

Non-expansive Mappings and Iterative Methods in Uniformly Convex Banach Spaces

In this article,we will investigate the properties of iterative sequence for non-expansive mappings and present several strong and weak convergence results of successive approximations to fixed points of non-expansive mappings in uniformly convex Banach spaces.The results presented in this article generalize and improve various ones concerned with constructive techniques for the fixed points of non-expansive mappings.

Coarse Embedding into Uniformly Convex Banach Spaces

In this paper, the author studies the coarse embedding into uniformly convex Banach spaces. The author proves that the property of coarse embedding into Banach spaces can be preserved under taking the union of the metric spaces under certain condi- tions. As an application, for a group G strongly relatively hyperbolic to a subgroup H, the author proves that B（n） = {g ∈ G／ │g│suЭe≤ n} admits a coarse embedding into a uniformly convex Banach space if H does.

A Weak Convergence Theorem for A Finite Family of Asymptotically Nonexpansive Mappings

The purpose of this paper is to prove a new weak convergence theorem for a finite family of asymptotically nonexpansive mappings in uniformly convex Banach space.

Ishikawa Iteration Process for Approximating Fixed Points of Nonexpansive Mappings

Let E be a uniformly convex Banach space which satisfies Opial’s conditionor has a Frechet differentiable norm.and C be a bounded closed convex subset of E.IfT:C→C is a nonexpansive mapping.then for any initial data x0∈C,the Ishikawaiteration process{xn},defined by xn=tnT(snTxn+(1-sn)xn)+(1-tn)xn,n≥0,converges weakly to a fixed point of T,where{tn}and{sn}are sequences in[0,1]withsome restrictions.

Weak and Strong Convergence for Fixed Points of Asymptotically Non-expansive Mappings

A few weak and strong convergence theorems of the modified three-step iterative sequence with errors and the modified Ishikawa iterative sequence with errors for asymptotically non-expansive mappings in any non-empty closed convex subsets of uniformly convex Banach spaces are established. The results presented in this paper substantially extend the results due to Chang (2001), Osilike and Aniagbosor (2000), Rhoades (1994) and Schu (1991).

A Variational Principle and Best Proximity Points

We generalize Ekeland＇s Variational Principle for cyclic maps. We present applications of this version of the variational principle for proving of existence and uniqueness of best proximity points for different classes of cyclic maps.