收缩投影法与涉及Hemi-相对相对非扩张映象的广义平衡问题的强收敛性

Motivated by the recent result obtained by Takahashi and Zembayashi in 2008,we prove a strong convergence theorem for finding a common element of the set of solutions of a generalized equilibrium problem and the set of fixed points of a hemi-relatively nonexpansive mapping in a Banach space by using the shrinking projection method.The main results obtained in this paper extend some recent results.     

Modified block iterative method for solving convex feasibility problem,equilibrium problems and variational inequality problems

The purpose of this paper is by using the modified block iterative method to propose an algorithm for finding a common element in the intersection of the set of common fixed points of an infinite family of quasi-φ-asymptotically nonexpansive and the set of solutions to an equilibrium problem and the set of solutions to a variational inequality. Under suitable conditions some strong convergence theorems are established in 2-uniformly convex and uniformly smooth Banach spaces. As applications we utilize the results presented in the paper to solving the convex feasibility problem (CFP) and zero point problem of maximal monotone mappings in Banach spaces. The results presented in the paper improve and extend the corresponding results announced by many authors.     

A unified approach to the weighted Grtzsch and Nitsche problems for mappings of finite distortion

This note deals with the existence and uniqueness of a minimiser of the following Grtzsch-type problem inf f ∈F∫∫_(Q_1)φ(K(z,f))λ(x)dxdyunder some mild conditions,where F denotes the set of all homeomorphims f with finite linear distortion K(z,f)between two rectangles Q_1 and Q_2 taking vertices into vertices,φ is a positive,increasing and convex function,and λ is a positive weight function.A similar problem of Nitsche-type,which concerns the minimiser of some weighted functional for mappings between two annuli,is also discussed.As by-products,our discussion gives a unified approach to some known results in the literature concerning the weighted Grtzsch and Nitsche problems.     

C^N中多项式自同构的动力系统

This paper is assigned to discuss the dynamics of a special class of polynomial automorphisms of C^N which was shown to be dense in the group of the polynomial automorphisms.We give some results about the analytic and geometric properties of the filled-in Julia set and the nonwandering set.We also make a characterization of the stable and unstable manifold for the filled-in Julia set.Furthermore,the number of the fixes points for such maps is studied.     

Hilbert空间中涉及一类新的具误差迭代程序的平衡问题的黏性逼近法

In this paper, we introduce an iterative scheme with error by the viscosity approximation method for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a nonexpansive mapping in a Hilbert space. A strong convergence theorem is given, which generalizes all the results obtained by S.Takahashi and W.Takahashi in 2007. In addition, some of the methods applied in this paper improve those of S.Takahashi and W.Takahashi.     

在Banach空间关于变分不等式和相对非扩张映射的弱收敛

In this paper, we introduce an iterative sequence for finding a common element of the set of fixed points of a relatively nonexpansive mapping and the set of solutions of the variational inequality for an inverse-strongly-monotone mapping in a Banach space. Then we show that the sequence converges weakly to a common element of two sets.     

APPROXIMATION OF COMMON SOLUTIONS OF VARIATIONAL INEQUALITIES VIA STRICT PSEUDOCONTRACTIONS

In this paper, a convex feasibility problem is considered. We construct an iterative method to approximate a common element of the solution set of classical variational inequalities and of the fixed point set of a strict pseudocontraction. Strong convergence theorems for the common element are established in the framework of Hilbert spaces.     

Zero-sum stochastic games with average payoffs: New optimality conditions

In this paper we study zero-sum stochastic games. The optimality criterion is the long-run expected average criterion, and the payoff function may have neither upper nor lower bounds. We give a new set of conditions for the existence of a value and a pair of optimal stationary strategies. Our conditions are slightly weaker than those in the previous literature, and some new sufficient conditions for the existence of a pair of optimal stationary strategies are imposed on the primitive data of the model. Our results are illustrated with a queueing system, for which our conditions are satisfied but some of the conditions in some previous literatures fail to hold.     

2一致凸Banach空间中均衡问题、变分不等式问题和不动点问题的一个弱收敛定理

In this paper,we introduce a new iterative scheme for finding the common element of the set of solutions of an equilibrium problem,the set of solutions of variational inequalities for an α-inversely strongly monotone operator and the set of fixed points of relatively nonexpansive mappings in a real uniformly smooth and 2-uniformly convex Banach space.Some weak convergence theorems are obtained,to extend the previous work.     

Hilbert投影距离与Banach空间的范数

In this paper, we establish some relations between the Hilbert＇s projective metric and the norm on a Banach space and show that the metric and the norm induce equivalent convergences at certain set. As applications, we utilize the main results to discuss the eigenvalue problems for a class of positive homogeneous operators of degree a and the positive solutions for a class of nonlinear algebraic system.     

Hilbert空间中关于变分不等式问题和不动点问题的粘性隐式中点算法

该文在Hilbert空间中研究了关于两个逆强单调算子的一般变分不等式问题和非扩张映射的不动点问题的粘性隐式中点算法,用修改的超梯度方法,在对参数作适当的限制下,得到了强收敛定理,所得结果推广和提高了许多最新文献中的相应结果.     

Hilbert空间上新的变分不等式问题和不动点问题的粘性迭代算法

本文在Hilbert空间上引入了一个新的粘性迭代算法,找到了关于两个逆强单调算子的变分不等式问题的解集与非扩张映射的不动点集的公共元.通过修改的超梯度算法,得到了强收敛定理,也给出了一个数值例子.所得结果改进了许多最新结果.     

Banach空间中关于平衡问题与半相对非扩张映象的强收敛定理

在Banach空间框架下,将半相对非扩张映象引入到平衡问题中,利用收缩投影迭代来近似平衡问题的解集与半相对非扩张映象的不动点集的公共点,并在适当的条件下证明了该迭代序列强收敛于某个公共点.所得的结果推广和改进了已有的相关结果.     

关于带扰动映像的广义平衡问题与k-严格伪压缩映像的不动点问题的强收敛定理

在Hilbert空间中提出一种新的迭代算法,用于寻求带扰动映像的广义平衡问题与k-严格伪压缩映像的不动点问题的公共解.此外,证明了由此迭代算法生成的序列的强收敛性.所得到的结果,推广并改进了最近一些人所发布的新结果.     

Approximating a Zero of Sum of Two Monotone Operators Which Solves a Fixed Point Problem in Reflexive Banach Spaces

Abstract

The purpose of this paper is to introduce an iterative method for approximating a point in the set of zeros of the sum of two monotone mappings, which is also a solution of a fixed point problem for a Bregman strongly nonexpansive mapping in a real reflexive Banach space. With our iterative technique, we state and prove a strong convergence theorem for approximating an element in the intersection of the set of solutions of a variational inclusion problem for sum of two monotone mappings and the set of solutions of a fixed point problem for Bregman strongly nonexpansive mapping. We give applications of our result to convex minimization problem, convex feasibility problem, variational inequality problem, and equilibrium problem. Our result complements and extends some recent results in literature.     

关于多正解问题的某些研究

本文以ｆｐ 同伦方法为工具，借助于一些适当的变换，研究有序的（Ｂ）空间中的集值映象方程的多正解问题；在文中的有关工作中，还使用了集值映象的拟导数的某些性质．     

一类集值映射的向量均衡问题

在拓扑向量空间内,研究了一类新的集值映射的广义向量均衡问题,利用KKM定理,证明了解的几个存在性定理,并讨论了解的性状.所得结果推广了近期一些作者的研究成果.     

关于Banach空间中增生和伪压缩型映象迭代序列的收敛性问题

得出了Banach空间中增生和伪压缩型映象Ishikawa、Mann和最速下降序列强收敛于其不动点的充分必要条件.所得结果推广、改进和包含了某些最新的结果.     

关于非扩张映象的最近的公共不动点问题

利用粘性逼近方法,在自反Banach空间的框架下,研究无限族非扩张映象及对给定的压缩映象的迭代程序的收敛性问题．在适当的条件下,证明了该迭代序列强收敛于某一公共不动点,而且这一公共不动点也是自反Banach空间中某一变分不等式的唯一解．所得结果改进和推广了一些人的最新的结果．