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VISCOSITY APPROXIMATION METHODS FOR THE SPLIT EQUALITY COMMON FIXED POINT PROBLEM OF QUASI-NONEXPANSIVE OPERATORS 认领 引用 被引量：1
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作者 赵静 王盛楠 《Acta Mathematica Scientia》 SCIE CSCD 2016年第5期1474-1486,共13页
Let H;, H;, H;be real Hilbert spaces, let A : H;→ H;, B : H;→ H;be two bounded linear operators. The split equality common fixed point problem（SECFP） in the infinite-dimensional Hilbert spaces introduced by Moudaf... Let H;, H;, H;be real Hilbert spaces, let A : H;→ H;, B : H;→ H;be two bounded linear operators. The split equality common fixed point problem（SECFP） in the infinite-dimensional Hilbert spaces introduced by Moudafi（Alternating CQ-algorithm for convex feasibility and split fixed-point problems. Journal of Nonlinear and Convex Analysis）is to find x ∈ F（U）, y ∈ F（T） such that Ax = By,（1）where U : H;→ H;and T : H;→ H;are two nonlinear operators with nonempty fixed point sets F（U） = {x ∈ H;: Ux = x} and F（T） = {x ∈ H;: Tx = x}. Note that,by taking B = I and H;= H;in（1）, we recover the split fixed point problem originally introduced in Censor and Segal. Recently, Moudafi introduced alternating CQ-algorithms and simultaneous iterative algorithms with weak convergence for the SECFP（1） of firmly quasi-nonexpansive operators. In this paper, we introduce two viscosity iterative algorithms for the SECFP（1） governed by the general class of quasi-nonexpansive operators. We prove the strong convergence of algorithms. Our results improve and extend previously discussed related problems and algorithms. 展开更多
关键词 split equality common fixed point problems quasi-nonexpansive operator strong convergence viscosity iterative algorithms Hilbert space
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FURTHER INVESTIGATION INTO APPROXIMATION OF A COMMON SOLUTION OF FIXED POINT PROBLEMS AND SPLIT FEASIBILITY PROBLEMS 认领 引用 被引量：2
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作者 Y.SHEHU O.T.MEWOMO F.U.OGBUISI 《Acta Mathematica Scientia》 SCIE CSCD 2016年第3期913-930,共18页
The purpose of this paper is to study and analyze an iterative method for finding a common element of the solution set ~ of the split feasibility problem and the set F（T） of fixed points of a right Bregman strongly ... The purpose of this paper is to study and analyze an iterative method for finding a common element of the solution set ~ of the split feasibility problem and the set F（T） of fixed points of a right Bregman strongly nonexpansive mapping T in the setting of p- uniformly convex Banach spaces which are also uniformly smooth. By combining Mann＇s iterative method and the Halpern＇s approximation method, we propose an iterative algorithm for finding an element of the set F（T）∩Ω moreover, we derive the strong convergence of the proposed algorithm under appropriate conditions and give numerical results to verify the efficiency and implementation of our method. Our results extend and complement many known related results in the literature. 展开更多
关键词 strong convergence split feasibility problem uniformly convex uniformly smooth fixed point problem right Bregman strongly nonexpansive mappings
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Strong Convergence of a General Iterative Algorithm for Mixed Equilibrium, Variational Inequality and Common Fixed Points Problems 认领 引用
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作者 Tanakit Thianwan 《Advances in Pure Mathematics》 2013年第1期83-98,共16页
The aim of this paper, is to introduce and study a general iterative algorithm concerning the new mappings which the sequences generated by our proposed scheme converge strongly to a common element of the set of solut... The aim of this paper, is to introduce and study a general iterative algorithm concerning the new mappings which the sequences generated by our proposed scheme converge strongly to a common element of the set of solutions of a mixed 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 a relaxed cocoercive mapping in a real Hilbert space. In addition, we obtain some applications by using this result. The results obtained in this paper generalize and refine some known results in the current literature. 展开更多
关键词 Nonexpansive Mapping Mixed Equilibrium Problem Variational Inequality Common Fixed Points Strong Convergence
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Self-Adaptive Algorithms for the Split Common Fixed Point Problem of the Demimetric Mappings 认领 引用 被引量：1
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作者 Xinhong Chen Yanlai Song +1 位作者 Jianying He Liping Gong 《Journal of Applied Mathematics and Physics》 2019年第10期2187-2199,共13页
The split common fixed point problem is an inverse problem that consists in finding an element in a fixed point set such that its image under a bounded linear operator belongs to another fixed-point set. In this paper... The split common fixed point problem is an inverse problem that consists in finding an element in a fixed point set such that its image under a bounded linear operator belongs to another fixed-point set. In this paper, we present new iterative algorithms for solving the split common fixed point problem of demimetric mappings in Hilbert spaces. Moreover, our algorithm does not need any prior information of the operator norm. Weak and strong convergence theorems are given under some mild assumptions. The results in this paper are the extension and improvement of the recent results in the literature. 展开更多
关键词 Hilbert Space Demimetric Mapping Split Common Fixed Point Problem Self-Adaptive Algorithm
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BREGMAN PROJECTIONS AND PARALLEL LINESEARCH ALGORITHMS FOR MULTIPLE-SETS PROBLEMS 认领 引用
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作者 Fahimeh Akhavan GHASSABZADE Zeynab JOUYMANDI Fridoun MORADLOU 《Acta Mathematica Scientia》 SCIE CSCD 2026年第4期1979-1998,共20页
In this article,using Bregman projections,we present parallel linesearch algorithms for finding the solution of the split common null point problem,the multiple-sets split equilibrium problem and the solution of the m... In this article,using Bregman projections,we present parallel linesearch algorithms for finding the solution of the split common null point problem,the multiple-sets split equilibrium problem and the solution of the multiple-sets split variational inequality problem in uniformly smooth and p-uniformly convex Banach spaces.To prove the strong convergence of the iterates generated by our algorithms,we do not need any auxiliary equilibrium problem.To demonstrate the applicability of our results,we present some numerical examples.To solve the minimization subproblems in our algorithms,we use the fmincon optimization toolbox in MATLAB R2015a. 展开更多
关键词 Bregman projection multiple-sets split equilibrium problem parallel linesearch method split common null point problem
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An Iterative Method for Split Variational Inclusion Problem and Split Fixed Point Problem for Averaged Mappings 认领 引用
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作者 Kaiwen Wang Yali Zhao Ziru Zhao 《Journal of Applied Mathematics and Physics》 2023年第6期1541-1556,共16页
In this paper, we use resolvent operator technology to construct a viscosity approximate algorithm to approximate a common solution of split variational inclusion problem and split fixed point problem for an averaged ... In this paper, we use resolvent operator technology to construct a viscosity approximate algorithm to approximate a common solution of split variational inclusion problem and split fixed point problem for an averaged mapping in real Hilbert spaces. Further, we prove that the sequences generated by the proposed iterative method converge strongly to a common solution of split variational inclusion problem and split fixed point problem for averaged mappings which is also the unique solution of the variational inequality problem. The results presented here improve and extend the corresponding results in this area. 展开更多
关键词 Split Variational Inclusion Problem Split Fixed Point Problem Iterative Algorithm Averaged Mapping Convergence
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Convergence Theorem of Hybrid Iterative Algorithm for Equilibrium Problems and Fixed Point Problems of Finite Families of Uniformly Asymptotically Nonexpansive Semigroups 认领 引用
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作者 Hongbo Liu Yi Li 《Advances in Pure Mathematics》 2014年第6期244-252,共9页
Throughout this paper, we introduce a new hybrid iterative algorithm for finding a common element of the set of common fixed points of a finite family of uniformly asymptotically nonexpansive semigroups and the set of... Throughout this paper, we introduce a new hybrid iterative algorithm for finding a common element of the set of common fixed points of a finite family of uniformly asymptotically nonexpansive semigroups and the set of solutions of an equilibrium problem in the framework of Hilbert spaces. We then prove the strong convergence theorem with respect to the proposed iterative algorithm. Our results in this paper extend and improve some recent known results. 展开更多
关键词 Hybrid Iterative Algorithm Uniformly Asymptotically Nonexpansive Semigroups Equilibrium Problem Common Fixed Point
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巴拿赫空间中广义分裂不动点问题的强收敛性 认领 引用
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作者 陈丽君 《闽江学院学报》 2026年第2期8-19,共12页
在巴拿赫空间中研究更具一般性的广义分裂不动点问题,构造了一种关于Bregman全局拟渐近非扩张映射的新迭代算法,并在适当条件下证明了该算法产生的序列强收敛于广义分裂不动点问题解集中的一点。最后,由上述结论给出了均衡问题与极大单... 在巴拿赫空间中研究更具一般性的广义分裂不动点问题,构造了一种关于Bregman全局拟渐近非扩张映射的新迭代算法,并在适当条件下证明了该算法产生的序列强收敛于广义分裂不动点问题解集中的一点。最后,由上述结论给出了均衡问题与极大单调算子零点问题的算法强收敛定理。 展开更多
关键词 广义分裂不动点问题 巴拿赫空间 Bregman全局拟渐近非扩张映射 强收敛性
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Further Investigation into Split Common Fixed Point Problem for Demicontractive Operators 认领 引用
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作者 Yekini SHEHU Oluwatosin T.MEWOMO 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2016年第11期1357-1376,共20页
Our contribution in this paper is to propose an iterative algorithm which does not reqmre prior knowledge of operator norm and prove strong convergence theorem for approximating a solution of split common fixed point ... Our contribution in this paper is to propose an iterative algorithm which does not reqmre prior knowledge of operator norm and prove strong convergence theorem for approximating a solution of split common fixed point problem of demicontractive mappings in a real Hilbert space. So many authors have used algorithms involving the operator norm for solving split common fixed point problem, but as widely known the computation of these Mgorithms may be difficult and for this reason, authors have recently started constructing iterative algorithms with a way of selecting the step-sizes such that the implementation of the algorithm does not require the calculation or estimation of the operator norm. We introduce a new algorithm for solving the split common fixed point problem for demicontractive mappings with a way of selecting the step-sizes such that the implementation of the Mgorithm does not require the calculation or estimation of the operator norm and then prove strong convergence of the sequence in real Hilbert spaces. Finally, we give some applications of our result and numerical example at the end of the paper. 展开更多
关键词 Demicontractive mappings split common fixed point problems iterative scheme strongconvergence Hilbert spaces
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Implicit iterative algorithms of the split common fixed point problem for Bregman quasi-nonexpansive mapping in Banach spaces 认领 引用
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作者 Yuanheng WANG Chanjuan PAN 《Frontiers of Mathematics in China》 SCIE CSCD 2022年第5期797-811,共15页
In this paper,we study a modified implicit rule for finding a solution of split common fixed point problem of a Bregman quasi-nonexpansive mapping in Banach spaces.We propose a new iterative algorithm and prove the st... In this paper,we study a modified implicit rule for finding a solution of split common fixed point problem of a Bregman quasi-nonexpansive mapping in Banach spaces.We propose a new iterative algorithm and prove the strong convergence theorem under appropriate conditions.As an application,the results are applied to solving the zero problem and the equilibrium problem. 展开更多
关键词 Split common fixed point implicit rule Bregman quasi-nonexpansive mapping strong convergence Banach space
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巴拿赫空间中分裂公共不动点问题的迭代逼近 认领 引用
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作者 陈丽君 《闽南师范大学学报（自然科学版）》 2025年第1期116-123,共8页
在巴拿赫空间中研究关于渐近严格伪压缩映射的分裂公共不动点问题,提出一种新的迭代算法,并在不同参数条件下证明了该算法的弱收敛与强收敛定理。最后将该算法进一步应用到解决分层变分不等式问题的解集中,并得到了对应的收敛定理。
关键词 渐近严格伪压缩映射 分裂公共不动点问题 巴拿赫空间 收敛性
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分裂可行性问题解集和有限族拟非扩张算子公共不动点集的公共元的迭代算法 认领 引用
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作者 张玉婷 高兴慧 彭剑英 《数学物理学报（A辑）》 CSCD 北大核心 2025年第1期256-268,共13页
在Hilbert空间中,构造了寻找分裂可行性问题与有限族拟非扩张算子公共不动点问题之公共解的一种新算法.在适当的条件下,利用映射的次闭性和投影算子与共轭算子的性质证明了由该算法生成的迭代序列强收敛到分裂可行性问题和不动点问题的... 在Hilbert空间中,构造了寻找分裂可行性问题与有限族拟非扩张算子公共不动点问题之公共解的一种新算法.在适当的条件下,利用映射的次闭性和投影算子与共轭算子的性质证明了由该算法生成的迭代序列强收敛到分裂可行性问题和不动点问题的公共解,并给出具体的数值实验验证算法的有效性.所得结果改进和推广了一些最新文献的相关结果. 展开更多
关键词 分裂可行性问题 不动点问题 有限族拟非扩张算子
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AN ITERATIVE METHOD FOR SPLIT VARIATIONAL INCLUSION PROBLEM AND FIXED POINT PROBLEM FOR A FAMILY OF GENERALIZED ASYMPTOTICALLY NONEXPANSIVE SEMIGROUP 认领 引用
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作者 Lijun Chen 《Annals of Applied Mathematics》 2017年第2期139-154,共16页
In this paper, strong convergence of an iterative sequence is proved, which computes an approximate solution of the set of solutions of split variational inclusion problem, the set of fixed points of a nonexpansive ma... In this paper, strong convergence of an iterative sequence is proved, which computes an approximate solution of the set of solutions of split variational inclusion problem, the set of fixed points of a nonexpansive mapping and the set of common fixed points of a family of generalized asymptotically nonexpansive semigroup. Results obtained in this paper extend and unify the previously known results in the previous literatures. 展开更多
关键词 split variational inclusion problem strong convergence theo rem fixed point problems generalized asymptotically nonexpansive semigroup
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希尔伯特空间中分裂等式不动点问题的强收敛性 认领 引用 被引量：1
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作者 陈汝栋 张辉文 +1 位作者 王洁 王亚琴 《西南大学学报（自然科学版）》 CAS CSCD 北大核心 2015年第12期80-84,共5页
介绍和研究了无穷维希尔伯特空间中分裂等式公共不动点的一个新的迭代方法.在适当的条件下,证明了由新算法生成的序列强收敛于分裂等式公共不动点问题的一个解.最后,将结论应用到分裂等式问题和变分问题中.
关键词 分裂等式不动点问题 分裂等式问题 强收敛
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Hilbert空间中关于不动点问题,变分不等式系统和分裂均衡问题迭代算法的强收敛定理 认领 引用 被引量：3
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作者 潘灵荣 王元恒 《数学物理学报（A辑）》 CSCD 北大核心 2023年第6期1880-1896,共17页
在Hilbert空间中,考虑渐近非扩张映像的不动点问题,变分不等式系统和分裂均衡问题的一个公共解.在适当的参数限制条件下,证明了所构造的修正粘性迭代序列强收敛到以上三类问题的一个公共元,所得结论改进和推广了一些最近文献的相关结果.
关键词 渐近非扩张映像 变分不等式系统 分裂均衡问题 不动点问题
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涉及拟反向强单调算子零点的一个弱收敛结果及其应用 认领 引用 被引量：1
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作者 杨延涛 陈晶晶 周海云 《浙江大学学报（理学版）》 CAS CSCD 北大核心 2022年第1期49-52,共4页
采用经典的最速下降法构造一类Lipschitz连续的拟反向强单调算子的零点,在相当宽松柔和的条件下,建立了一个弱收敛结果。将弱收敛定理应用于分裂公共不动点问题,所得结果改进了近期文献的相应结果。
关键词 拟反向强单调算子 最速下降法 弱收敛 分裂公共不动点问题
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Banach空间中分裂变分包含问题和分裂不动点问题的迭代算法 认领 引用 被引量：1
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作者 赵亚莉 李新昊 +1 位作者 王凯文 于嘉欣 《渤海大学学报（自然科学版）》 CAS 2024年第1期41-52,共12页
提出了一种新的迭代算法,求解一致凸光滑Banach空间中非扩张映射分裂不动点问题和分裂变分包含问题.在适当的条件下,证明了该算法的强收敛性定理.所得结果改进和推广了相关文献的相应结果.
关键词 Banach空间 分裂变分包含问题 分裂不动点问题 非扩张映射 收敛性
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分层混合均衡问题和不动点问题的等价性 认领 引用 被引量：1
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作者 闻道君 张蓉 宋树枝 《西南大学学报（自然科学版）》 CAS CSCD 北大核心 2018年第8期110-113,共4页
在Hilbert空间中,介绍了一类改进的混合均衡问题,并在适当条件下研究了混合均衡问题与不动点问题的等价关系,进一步建立了关于分层混合均衡问题解的一个充分必要条件.
关键词 分层混合均衡问题 不动点 等价关系 Hilbert空间
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Banach空间中Bregman拟非扩张映射分裂公共不动点的隐式迭代算法 认领 引用 被引量：2
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作者 王元恒 潘婵娟 《数学进展》 CSCD 北大核心 2022年第4期704-716,共13页
本文在Banach空间中研究了关于Bregman拟非扩张映射的分裂公共不动点问题的修正隐式法则,给出了一种新的迭代算法,在一定条件下证明了迭代序列的强收敛定理.作为应用,将所得的结果应用于零点问题和均衡问题的求解.
关键词 分裂公共不动点 隐式法则 Bregman拟非扩张映射 强收敛 Banach空间
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一类弱非线性互补问题的模系矩阵多分裂迭代算法 认领 引用 被引量：11
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作者 夏泽晨 李郴良 《桂林电子科技大学学报》 2015年第3期255-258,共4页
针对一类求解弱非线性互补问题,提出了模系矩阵多分裂迭代算法。通过变量变换,利用互补向量的性质,将互补问题转化为一类与其等价的不动点方程组。在此基础上,建立一种快速、有效的模系矩阵多分裂迭代算法,并分析了算法的收敛性。数值... 针对一类求解弱非线性互补问题,提出了模系矩阵多分裂迭代算法。通过变量变换,利用互补向量的性质,将互补问题转化为一类与其等价的不动点方程组。在此基础上,建立一种快速、有效的模系矩阵多分裂迭代算法,并分析了算法的收敛性。数值实验证明了算法的有效性。 展开更多
关键词 弱非线性互补问题 模系数矩阵分裂 不动点方程组
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