On the weak convergence of iterative sequences for generalized equilibrium problems and strictly pseudocontractive mappings

In this article we consider the problem of finding a common element in the solution set of generalized equilibrium problems, in the solution set of the classical variational inequality and in the fixed point set of strictly pseudocontractive mappings. Weak convergence theorems of common elements are established in real Hilbert spaces.     

非扩张映射的不动点与变分包含问题的公共解

In this paper, we introduce an iterative scheme for finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inclusion for an inverse-strongly monotone mapping and a maximal monotone mapping in a real Hilbert space. Then we show that the sequence converges strongly to a common element of two sets. Using the result, we consider the problem of finding a common fixed point of a nonexpansive mapping and a strictly pseudocontractive mapping in a real Hilbert space.     

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.     

Convergence theorems of common elements for equilibrium problems and fixed point problems

In this paper, we introduce an iterative method for finding a common element of the set of solutions of an equilibrium problem, the set of common fixed points of two asymptotically nonexpansive mappings in a Hilbert space. We show that the iterative sequence converges strongly to a common element of the two sets.     

Some results on generalized equilibrium problems involving strictly pseudocontractive mappings

In this paper,we consider an iterative sequence for generalized equilibrium problems and strictly pseudocontractive mappings.We show that the iterative sequence converges strongly to a common element of the solution set of generalized equilibrium problems and of the fixed point set of strictly pseudocontractive mappings.     

Weak convergence theorem for monotone mappings and a countable family of nonexpansive mappings

In this paper, we introduce an iterative process for finding the common element of the set of common fixed points of a countable family of nonexpansive mappings and the set of solutions of the variational inequality problem for an α$\alpha$-inverse-strongly-monotone mapping. We obtain a weak convergence theorem for a sequence generated by this process. Moreover, we apply our result to the problem for finding a common element of the set of equilibrium problems and the set of solutions of the variational inequality problem of a monotone mapping.     

An extragradient method for relaxed cocoercive variational inequality and equilibrium problems

The purpose of this paper is to investigate the problem of finding the common element of the set of common fixed points of a countable family of nonexpansivemappings, the set of an equilibrium problem and the set of solutions of the variational inequality problem for a relaxed cocoercive and Lipschitz continuous mapping in Hilbert spaces. Then, we show that the sequence converges strongly to a common element of the above three sets under some parameter controlling conditions, which are connected with Yao, Liou, Yao, Takahashi and many others.     

Construction of Iterative Methods for Variational Inequality and Fixed Point Problems

In this article, we first introduce two iterative methods for finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality for an inverse strongly monotone mapping in a Hilbert space. Then we show that the proposed iterative methods converge strongly to a minimum norm element of two sets.     

A hybrid approximation method for equilibrium and fixed point problems for a monotone mapping and a nonexpansive mapping

The purpose of this paper is to present an iterative scheme by a hybrid method for finding a common element of the set of fixed points of a nonexpansive mapping, the set of solutions of an equilibrium problem and the set of solutions of the variational inequality for α-inverse-strongly monotone mappings in the framework of a Hilbert space. We show that the iterative sequence converges strongly to a common element of the above three sets under appropriate conditions. Additionally, the idea of our results are applied to find a zero of a maximal monotone operator and a strictly pseudocontractive mapping in a real Hilbert space.     

Strong convergence theorems by hybrid methods for a finite family of nonexpansive mappings and inverse-strongly monotone mappings

In this paper, we introduce and study an iterative scheme by a hybrid method for finding a common element of the set of solutions of an equilibrium problem, the set of common fixed points of a finite family of nonexpansive mappings and the set of solutions of the variational inequality for an inverse-strongly-monotone mapping in a real Hilbert space. Then, we prove that the iterative sequence converges strongly to a common element of the three sets. Using this result, we consider the problem of finding a common fixed point of a finite family of nonexpansive mappings and a strictly pseudocontractive mapping and the problem of finding a common element of the set of common fixed points of a finite family of nonexpansive mappings and the set of zeros of an inverse-strongly monotone mapping. The results obtained in this paper extend and improve the several recent results in this area.     

带扰动映像的广义平衡问题和不动点问题的混合粘性逼近问题

引入一个用于寻求带扰动映像的广义平衡问题解集以及可数无穷多非扩张映像之族公共不动点集的公共解的新的迭代算法. 证明了由此算法生成的序列的强收敛性. 所得的结果推广改进了先前许多作者的结果.     

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.     

关于变分包含问题和不动点问题的一些结果及应用

基于一个广义迭代算法,考虑了逼近一类拟变分包含问题解集与一族无限多个非扩张映象公共不动点集的某一公共元问题.在实Hilbert空间的框架下,证明了由次广义迭代算法产生的迭代序列强收敛到某一公共元.     

Convergence theorems based on hybrid methods for generalized equilibrium problems and fixed point problems

The purpose of this work is to introduce a hybrid projection method for finding a common element of the set of a generalized equilibrium problem, the set of solutions to a variational inequality and the set of fixed points of a strict pseudo-contraction in a real Hilbert space.     

广义平衡问题与非扩张映象不动点问题公解的一个新迭代方法

In this paper,we introduce a new iterative scheme for finding a common element of the set of solutions for a generalized equilibrium problems and the set of fixed points for nonexpansive mappings in Hilbert space.Under suitable conditions,some strong convergence theorems are proved.Our results extend and improve some recent results.     

Three-step iterations for variational inequalities and nonexpansive mappings

In this paper, we introduce a new three-step iterative scheme for finding the common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality using the technique of updating the solution. We show that the sequence converges strongly to a common element of two sets under some control conditions. Results proved in this paper may be viewed as an improvement and refinement of the recent results of Noor and Huang [M. Aslam Noor, Z. Huang, Three-step methods for nonexpansive mappings and variational inequalities, Appl. Math. Comput., in press] and Yao and Yao [Y. Yao, J.C. Yao, On modified iterative method for nonexpansive mappings and monotone mappings, Appl. Math. Comput., in press].     

Some results on generalized equilibrium problems involving a family of nonexpansive mappings

In this paper, we introduce an iterative method for finding a common element in the solution set of generalized equilibrium problems, in the solution set of variational inequalities and in the common fixed point set of a family of nonexpansive mappings. Strong convergence theorems are established in the framework of Hilbert spaces.     

一般变分包含和不动点问题的黏性迭代算法

借助黏性方法在Hilbert空间的框架下介绍一种迭代程序用以寻求具多值极大单调映象和逆强单调映象的变分包含的解集及非扩张映象的不动点集的公共元.改进和推广了一些人的新结果.     

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.     

无限族demi压缩映射与平衡问题的收敛定理

在Hilbert空间中,为了找到无限个demi压缩映射公共不动点集和广义混合平衡问题解的公共元,本文介绍了一种迭代算法,得到关于公共元的强收敛定理,并给出例子说明结果.