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.     

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.     

关于变分不等式与不动点问题(英文)

In this paper,A strong convergence theorem for a finite family of nonexpansive mappings and relaxed cocoercive mappings based on an iterative method in the framework of Hilbert spaces is established.     

Banach空间无限族渐近非扩张映象黏性逼近法

In the framework of reflexive Banach spaces satisfying a weakly continuous duality map, the author uses the viscosity approximation method to obtain the strong convergence theorem for iterations with infinitely many asymptotically nonexpansive mappings. The main results obtained in this paper improve and extend some recent results.     

A NEW ITERATIVE METHOD FOR FINDING COMMON SOLUTIONS OF GENERALIZED EQUILIBRIUM PROBLEM, FIXED POINT PROBLEM OF INFINITE k-STRICT PSEUDO-CONTRACTIVE MAPPINGS, AND QUASI-VARIATIONAL INCLUSION PROBLEM

In this article,we introduce a hybrid iterative scheme for finding a common element of the set of solutions for a generalized equilibrium problems,the set of common fixed point for a family of infinite...     

求解一类广义Nash均衡问题

Generalized Nash equilibrium problem (GNEP) is an important model that has many applications in practice. However, a GNEP usually has multiple or even infinitely many Nash equilibrium points and it is not easy to choose a favorable solution from those equilibria. This paper considers a class of GNEP with some kind of separability. We first extend the so-called normalized equilibrium concept to the stationarity sense and then, we propose an approach to solve the normalized stationary points by reformulating the GNEP as a single optimization problem. We further demonstrate the proposed approach on a GNEP model in similar product markets.     

拟变分包含与不动点问题公共解的迭代算法

By introducing the resolvent operator associated with a maximal monotone mapping, the author obtains a strong convergence theorem of a generalized iterative algorithm for a class of quasi-variational inclusion problems, which extends and unifies some recent results.     

Banach空间中关于广义变分不等式组的一迭代算法

In this paper, we propose an iterative method of approximating solutions for a class of the system of generalized variational inequalities and give a convergence result for the iterative method in uniformly convex and uniformly smooth Banach spaces.     

有限个平衡问题与非扩张映象不动点问题的复合迭代方法

在Hilbert空间中引进并研究一种新的复合粘性迭代算法,借以寻求有限个平衡问题的公共解集与非扩张映象不动点集的一个公共元素.所得结果改进并推广了最近一些人的最新结果.     

拓扑空间中新的广义L-KKM型定理及其应用

In this paper, some new generalized L-KKM type theorems with finitely open values and with finitely closed values are established without any convexity structure in topological spaces. As applications, some new matching theorem, fixed point theorem and existence the orem of equilibrium problem with lower and upper bounds are also given under some suitable conditions. These theorems presented in this paper unify and generalize some corresponding known results in recent literatures.     

Hilbert空间中关于广义平衡问题与不动点问题公共解的收敛定理

本文在Hilbert空间中引进了一迭代方法来逼近两个集合的公共元素,这两个集合分别是一类广义平衡问题的解集和两个渐近非扩张映射公共不动点集.得到一强收敛定理,所得结果提高和推广了许多作者的相应结果.     

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.     

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.     

Hilbert空间中广义平衡问题和不动点问题的粘滞逼近法

在Hilbert空间,我们用粘滞逼近法建立了一迭代序列来逼近两个集合的公共点,这两个集合分别是广义平衡问题的解集和渐进非扩张映射的不动点集.我们表明这一迭代序列强收敛到这两个集合的公共点,而且这一公共点还是一变分不等式的解.用这一结果,还研究了三个强收敛问题和优化问题.     

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.     

Extragradient Methods for Solving Equilibrium Problems,Variational Inequalities,and Fixed Point Problems

In this paper, we propose the new extragradient algorithms for an α-inverse-strongly monotone operator and a relatively nonexpansive mapping in Banach spaces. We prove convergence theorems by this methods under suitable conditions. Applying our algorithms, we find a zero paint of maximal monotone operators. Using FMINCON optimization toolbox in MATLAB, we give an example to illustrate the usability of our results.     

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.     

广义平衡与不动点问题的黏性逼近

本文的目的是在Hilbert空间中引入和研究了一种新的迭代序列,用以寻求具逆一强单调映象的广义平衡问题的解集与无限簇非扩张映象的不动点集的公共元.在适当的条件下,用黏性逼近法证明了逼近于这一公共元的强收敛定理.应用该结论,我们证明了逼近于平衡问题和变分不等式问题的强收敛定理.所得结果改进和推广了文献的相应结果.