多值Bregman全拟渐近非扩张映像的强收敛性

建立了一种算法,用以寻求自反Banach空间中多值Bregman全拟渐近非扩张映像的有限族的公共不动点,改进和推广了以前的结果(算法是基于与一凸函数有关的Bregman距离).最后,把所得的结果应用于平衡系统问题,自反Banach空间中极大单调映像的零点问题.     

Banach空间中可数非扩张映像族公共不动点迭代算法

提出一种新的迭代算法用于求解实一致光滑Banach空间上可数非扩张映像族的公共不动点.在一定条件下证明了迭代算法产生的序列强收敛到一个公共不动点,并且此不动点也是一个变分不等式的解.此结果改进和推广了已有的相关结果.     

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.     

Banach空间中可数拟-φ-非扩张映像族的公共不动点的收敛定理

在某些Banach空间中针对一类闭的拟-φ-非扩张映像的可数无限族,修正经典的正规Mann迭代算法以达到强收敛的目标,所得结果改进并扩展了Matsushita和Takahashi等人的相关结果.     

弱相对非扩张映像不动点单调CQ算法与应用

Kamimura和Takahashi$^{[7]}$证明了相对非扩张映像CQ迭代算法的强收敛定理.该文构造了单调CQ算法, 用来逼近弱相对非扩张映像不动点, 证明了强收敛定理. 并将结果应用于逼近Banach空间极大单调算子的零点. 单调CQ算法比目前的CQ算法收敛速度快. 另外, 为证明弱相对非扩张映像不动点强收敛定理,该文运用了新的Cauchy列证明方法, 而不用Kadec-Klee性质, 该文结果改进了S.Matsushita 和 W.Takahashi及其它人的结果.     

A-线性Bregman 迭代算法

线性Bregman迭代是Osher和Cai等人最近提出的一种在压缩感知等领域有重要作用的有效算法.本文在矩阵A非满秩情形下,研究了求解下面最优化问题的线性Bregman迭代:min u∈R~M{‖u‖_1:Au+g}给出了一个关于线性Bregman迭代收敛性定理的简化证明,设计了一类A~-线性Bregman迭代算法,并针对A~+情形证明了算法的收敛性.最后,用数值仿真实验验证了本文算法的可行性.     

拟非扩张映像族的公共不动点的迭代方法

引入了修正的杂交投影迭代算法,用来构造Hilbert空间中拟非扩张映像族的公共不动点.使用新的算法证明了几个强收敛定理.新算法的优点是不要求映像具有次闭性质.     

非扩张映像不动点新的简单逼近算法

提出了一个简单的非扩张映像不动点的逼近算法,该算法通过非迭代的逼近序列来实现.从算法的复杂性来看,提出的算法比经典的Mann迭代算法、Ishikawa迭代算法和Halpern迭代算法更简单.提出的算法紧密联系着非扩张映像不动点的存在性,因此,还得到了非扩张映像的新不动点定理, 拓展和改进了经典的Goebel-Kirk,Kim-Xu等作者的结果.     

求解l1极小化问题的Bregman迭代算法

在Tikhonov正则化方法的基础上将其转化为一类l1极小化问题进行求解,并基于Bregman迭代正则化构建了Bregman迭代算法,实现了l1极小化问题的快速求解.数值实验结果表明,Bregman迭代算法在快速求解算子方程的同时,有着比最小二乘法和Tikhonov正则化方法更高的求解精度.     

无穷可数族非自射非扩张映象之公共不动点的带误差逼近问题

设E具Gateaux可微的严格凸的自反Banach空间,C是E的一非空闭凸子集.受姚永红等2007年文献[1]的启发.本文在此Banach空间框架下引进了一涉及无穷可数族非自射非扩张映象{T:C→E)<'∞><,t=1>的含误差的显式迭代算法,并且在非常少的限制条件下证明了该迭代序列的强收敛于无穷可数族非自射非扩张映象...     

CONVERGENCE ANALYSIS FOR SYSTEM OF EQUILIBRIUM PROBLEMS AND LEFT BREGMAN STRONGLY RELATIVELY NONEXPANSIVE MAPPING

In this paper, we prove strong convergence theorems for approximation of a fixed point of a left Bregman strongly relatively nonexpansive mapping which is also a solution to a finite system of equilibrium problems in the framework of reflexive real Banach spaces. We also discuss the approximation of a common fixed point of a family of left Bregman strongly nonexpansive mappings which is also solution to a finite system of equilibrium problems in reflexive real Banach spaces. Our results complement many known recent results in the literature.     

Convergence analysis for system of equilibrium problems and left bregman strongly relatively nonexpansive mapping

In this paper, we prove strong convergence theorems for approximation of a fixed point of a left Bregman strongly relatively nonexpansive mapping which is also a solution to a finite system of equilibrium problems in the framework of reflexive real Banach spaces. We also discuss the approximation of a common fixed point of a family of left Bregman strongly nonexpansive mappings which is also solution to a finite system of equilibrium problems in reflexive real Banach spaces. Our results complement many known recent results in the literature.     

Halpern's Iteration for Bregman Relatively Nonexpansive Mappings in Banach Spaces

In this article, using Bregman functions, we first introduce new modified Mann and Halpern's iterations for finding common fixed points of an infinite family of Bregman relatively nonexpansive mappings in the framework of Banach spaces. Furthermore, we prove the strong convergence theorems for the sequences produced by the methods. Finally, we apply these results for approximating zeroes of accretive operators. Our results improve and generalize many known results in the current literature.     

Strong Convergence Theorems for a Countable Family of Multi-Valued Bregman Quasi-Nonexpansive Mappings in Reflexive Banach Spaces

This article uses the shrinking projection method introduced by Takahashi, Kubota and Takeuchi to propose an iteration algorithm for a countable family of Bregman multi-valued quasi-nonexpansive mappings in order to have the strong convergence under a limit condition in the framework of reflexive Banach spaces. We apply our results to a zero point problem of maximal monotone mappings and equilibrium problems in reflexive Banach spaces. The results presented in the article improve and extend the corresponding results of that found in the literature.     

Approximation of common fixed points for a countable family of relatively nonexpansive mappings in a Banach space and applications

In this paper, we prove a strong convergence theorem by the hybrid method for a countable family of relatively nonexpansive mappings in a Banach space. We also establish a new control condition for the sequence of mappings {T_n} which is weaker than the control condition in Lemma 3.1 of Aoyama et al. [K. Aoyama, Y. Kimura, W. Takahashi and M. Toyoda, Approximation of common fixed points of a countable family of nonexpansive mappings in a Banach space, Nonlinear Anal. 67 (2007) 2350-2360]. Moreover, we apply our results for finding a common fixed point of two relatively nonexpansive mappings in a Banach space and an element of the set of solutions of an equilibrium problem in a Banach space, respectively. Our results are applicable to a wide class of mappings.     

Strongly relatively nonexpansive sequences in Banach spaces and applications

We introduce the concept of a strongly relatively nonexpansive sequence in a Banach space and investigate its properties. Then we apply our results to the problem of approximating a common fixed point of a countable family of relatively nonexpansive mappings in a uniformly convex and uniformly smooth Banach space.      

Strong convergence theorems for two countable families of weak relatively nonexpansive mappings and applications

The purpose of this article is to prove strong convergence theorems for common fixed points of two countable families of weak relatively nonexpansive mappings in Banach spaces. In order to get the strong convergence theorems, the monotone hybrid algorithms are presented and are used to approximate the common fixed points. Using this result, we also discuss the problem of strong convergence concerning the maximal monotone operators in a Banach space. The results of this article modify and improve the results of Matsushita and Takahashi [S. Matsushita, W. Takahashi, A strong convergence theorem for relatively nonexpansive mappings in a Banach space, J. Approx. Theory 134 (2005) 257-266] and the results of Plubtieng and Ungchittrakool [S. Plubtieng, K. Ungchittrakool, Strong convergence theorems for a common fixed point of two relatively nonexpansive mappings in a Banach space, J. Approx. Theory 149 (2007) 103-115] and the results of Su et al. [Y. Su, Z. Wang and H. Xu, Strong convergence theorems for a common fixed point of two hemi-relatively nonexpansive mappings, Nonlinear Anal. 71 (2009) 5616-5628], and many others.     

A hybrid extragradient method for solving pseudomonotone equilibrium problems using Bregman distance

In this paper, using a hybrid extragradient method, we introduce a new iterative process for approximating a common element of the set of solutions of equilibrium problems involving pseudomonotone bifunctions and the set of common fixed points of a finite family of multi-valued Bregman relatively nonexpansive mappings in the setting of reflexive Banach spaces. For this purpose, we introduce Bregman–Lipschitz-type condition for a pseudomonotone bifunction. It seems that these results for pseudomonotone bifunctions are first in reflexive Banach spaces. This paper concludes with certain applications, where we utilize our results to study the determination of a common point of the solution set of a variational inequality problem and the fixed point set of a finite family of multi-valued relatively nonexpansive mappings. A numerical example to support our main theorem will be exhibited.     

A general algorithm for multiple-sets split feasibility problem involving resolvents and Bregman mappings

In this paper, by using Bregman distance, we introduce a new iterative process involving products of resolvents of maximal monotone operators for approximating a common element of the set of common fixed points of a finite family of multi-valued Bregman relatively nonexpansive mappings and the solution set of the multiple-sets split feasibility problem and common zeros of maximal monotone operators. We derive a strong convergence theorem of the proposed iterative algorithm under appropriate situations. Finally, we mention several corollaries and two applications of our algorithm.     

Convergence theorem for equilibrium problem and Bregman strongly nonexpansive mappings in Banach spaces

In this paper, we present an iterative scheme for Bregman strongly nonexpansive mappings in the framework of Banach spaces. Furthermore, we prove the strong convergence theorem for finding common fixed points with the set of solutions of an equilibrium problem.