Nonlinear ergodic theorems of nonexpansive type mappings

Let S be a semitopological semigroup. Let C be a closed convex subset of a uniformly convex Banach space E whose norm is Fréchet differentiable and be a continuous representation of S as almost asymptotically nonexpansive type mapping of C into C such that the common fixed point set F(ℑ) of ℑ in C is nonempty. In this paper, we prove that if S is right reversible then for each x∈C, the closed convex set consists of at most one point. We also prove that if S is reversible, then the intersection is nonempty for each x∈C if and only if there exists a nonexpansive retraction P of C onto F(ℑ) such that PTt=TtP=P for all t∈S and Px is in the closed convex hull of for each x∈C.     

Convergence theorems of fixed points for asymptotically hemi-pseudocontractive mappings

In this paper, the concept of asymptotically hemi-pseudocontractive mapping in Banach space, which is a proper generalization of asymptotically pseudocontractive mapping with nonempty fixed point set as shown by an example, is introduced. Some sufficient and necessary conditions on the strong convergence of the modified Ishikawa and the modified Mann iteration sequences with mean errors for uniformly L-Lipshitzian asymptotically hemi-pseudocontractive mappings are presented.     

General alternative regularization methods for split equality common fixed-point problem

The purpose of this paper is to propose a general alternative regularization algorithm for split equality common fixed-point problem of nonexpansive operator in the framework of infinite-dimensional Hilbert spaces. We prove the strong convergence of the proposed algorithm with the stepsizes chosen by two ways. As a consequence, we obtain strong convergence theorems for split equality common fixed-point problem of firmly-nonexpansive operator and split equality problem. The efficiency of the proposed algorithms is illustrated by some numerical tests.     

A strong convergence theorem for solutions to a nonhomogeneous second order evolution equation

In this paper, we establish the strong convergence of possible solutions to the following nonhomogeneous second order evolution system

     

Weak and strong convergence theorems for a finite family of I-asymptotically nonexpansive mappings

In this paper, a new two-step iterative scheme for a finite family of I_i-asymptotically nonexpansive nonself-mappings is constructed in a uniformly convex Banach space. Weak and strong convergence theorems of this iterative scheme to a common fixed point of and are proved in a uniformly convex Banach space. The results of this paper improve and extend the corresponding results of Temir [2].     

Weak and strong convergence of the Ishikawa iterative process for a finite family of asymptotically nonexpansive mappings

In this paper, we introduce an Ishikawa implicit iterative process with errors for a finite family of N asymptotically nonexpansive mappings as follows:

     

极大单调算子和相对非扩展映射的修正杂交迭代算法

在实一致光滑、一致凸Banach空间中提出了两种修正杂交迭代算法,证明了迭代序列既强收敛到极大单调算子的零点, 又强收敛到非扩展映射的不动点的结论. 推广和补充了以往的研究工作.     

SOME GENERALIZATIONS OF KY FAN＇S BEST APPROXIMATION THEOREM

We pressent new Ky Fan type best approximation theorems for a discontinuous multivalued map onmetrizable topological vector spaces and hyperconvex spaces. In addition, fixed point results are derivedfor the map studied. Our work generalizes severl results in approximation theory.     

(渐近)非扩张映象的不动点的迭代逼近

Let E be a uniformly convex Banach space which satisfies Opial‘s condition or has aFrechet differentiable norm,and C be a bounded closed convex subset of E. If T： C→C is(asymptotically)nonexpansive,then the modified Ishikawa iteration process defined by     

关于超凸度量空间的几点注记

本文研究超凸度量空间的一些性质 ,给出更深入的结果及反例 .