广义均衡问题的算法及强收敛性——基于Wiener-Hopf方程技巧

利用广义Wiener-Hopf方程技巧构造了求解广义混合均衡问题、无限个非扩张映射的不动点问题及变分不等式问题的公共元的迭代算法,并在Hilbert空间中获得了两个强收敛定理.最后利用这些新算法研究了几类优化问题.以上方法和结果不同于前人并且推广了Shi和Noor的结果.     

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.     

Banach空间中广义平衡问题和一族相对非扩张映象的强收敛定理

在Banach空间中,用收缩投影的方法证明了广义平衡问题和一族相对非扩张映象的公共不动点的强收敛定理.结论改进了最近一些人的研究结果     

Hilbert空间中广义平衡问题与k-严格伪压缩映象的强收敛定理

在Hilbert空间中引进并研究了一种新的迭代算法,借以寻求广义平衡问题解集与k-严格伪压缩映象不动点集的一公共元.所得到的结果,推广并改进了最近一些人所发布的新结果.     

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.     

Hilbert空间中广义平衡问题和无限族非扩张映象的不动点问题的强收敛定理

在Hilbert空间中,用Fan-KKM定理导出了广义平衡问题的辅助问题的解的存在性和唯一性,讨论了寻找广义平衡问题和一族非扩张映象的公共不动点集的迭代序列,证明此序列强收敛于这两个集合的公共元.本文结论改进了一些近期结果.     

广义对策的一个新的平衡存在定理

在本文中，我们对具有不可数多个经纪人，具有非紧选择集和具有一般选择对应的广义对策证明了一个新的平衡存在定理。这用既不要求选择对应有开图也不要求它有开下截口。这个定理改进了Ｋｉｍ的一个最近结果。     

Convergence theorems for nonexpansive mappings and feasibility problems

In this paper, we introduce an iteration scheme given by finite nonexpansive mappings in Banach spaces and then prove weak convergence theorems which are connected with the problem of image recovery. Using the results, we consider the problem of finding a common fixed point of finite nonexpansive mappings.     

Convergence theorems for nonspreading mappings and nonexpansive multivalued mappings and equilibrium problems

In this paper, we introduce some new iterative sequences for finding a common element of the set of solutions of an equilibrium problem and the set of common fixed points of a finite family of nonspreading mappings and a finite family of nonexpansive multivalued mappings in Hilbert space. We establish some weak and strong convergence theorems of the sequences generated by our iterative process. The results obtained in this paper extend and improve some recent known results.     

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.     

Hilbert空间中混合平衡问题与非扩张半群的强收敛定理

在Hilbert空间中引进并研究了一种新的迭代算法,借以寻求混合平衡问题解集与非扩张半群不动点集的一公共元.所得到的结果,推广并改进了最近一些人所发布的新结果.     

Strong pseudo-convex mappings in dual problems

In this paper some relations between strong pseudo-convexity and other generalized convexity-properties of mappings (convex-likeness, quasi -convexity) into Banach-spaces are described. Furthermore necessary and sufficient conditions for the strong pseudo-convexity of a mapping are presented. Especially, sufficient conditions for the strong pseudo-convexity of composite mappings are proved. Applying these results a correct ion of a direct duality theorem given by Chandra and Lata is formulated.     

Generalized mildly nonlinear complementarity problems for fuzzy mappings

In this paper, we introduce and study a new class of generalized mildly nonlinear complementarity problems for fuzzy mappings. We use the change of variables technique to establish the equivalence between the generalized mildly nonlinear complementarity problems and the Wiener-Hopf equations. This equivalence is used to suggest and analyze a number of iterative algorithm for solving the generalized mildly nonlinear complementarity problems.     

关于m-值随机序列广义随机选择的一个强极限定理

§ 1.　Introduction　　ConsiderasequenceofBernoullitrials ,andsupposethatateachtrialthebettorhasthefreechoiceofwhetherornottobet.Asystemconsistsinfixedrulesselectingthosetrialsonwhichtheplayeristobet.ThetheoremongamblingsystemassertsthatunderanysystemthesuccessivebetsformasequenceofBernoullitrialwithunchangedprobabilityforsuccess.TheimportanceofthisstatementwasfirstrecognizedbyvonMises,whointroducedtheimpossibili tyofasuccessfulgamblingsystemasafundamentalaxiom(cf.[1 ],[2 ],[3],[4]) .Thecon …     

Equilibrium problems with set-valued mappings in Banach spaces

In this paper we consider two classes of equilibrium problems which imply general α$\alpha$-pseudomonotonicity and general α$\alpha$-semipseudomonotonicity relative to a set-valued map on reflexive and nonreflexive Banach spaces, respectively. Using the classical KKM technique, we obtain some existence results under boundedness as well as under unboundedness assumptions. Some examples are given.     

On Finite and Strong Convergence of a Proximal Method for Equilibrium Problems

We introduce the notions of conditioning and well-posedness for equilibrium problems. Using these concepts, we obtain finite and strong convergence results for the proximal method that improve, develop, and unify several theorems in optimization and nonlinear analysis.     

基于广义逆的矩阵Padé逼近的DeMontessus-De Ballore型收敛性定理

基于广义逆的矩阵Padé逼近[4,5]的一个行收敛性定理,即著名的DeMontessus-De     

广义均衡问题和严格伪压缩映像的收敛性定理及应用(英文)

本文运用平行算法,提出一种寻求广义均衡问题和严格伪压缩映像不动点集的公共元的迭代算法,并在Hilbert空间框架下证明了算法的强收敛性.进一步,将定理结果应用到凸可行性问题中.     

Strong Convergence Theorem for Multiple Sets Split Feasibility Problems in Banach Spaces

The purpose of this article is to study the iterative approximation of solution to multiple sets split feasibility problems in p-uniformly convex real Banach spaces that are also uniformly smooth. We propose an iterative algorithm for solving multiple sets split feasibility problems and prove a strong convergence theorem of the sequence generated by our algorithm under some appropriate conditions in p-uniformly convex real Banach spaces that are also uniformly smooth.