Banach空间中Ishikawa迭代序列的稳定性和收敛性问题

在Banach空间的框架下,讨论了中间意义下的渐进非扩张的渐进伪压缩的具平均误差的修正的Ishikawa和Mann迭代序列的收敛性和稳定性之间的等价性问题,改进和推广了以前的结果.     

Strong Convergence Theorems for a Finite Family of Sequences of Nearly Nonexpansive Mappings in Hilbert Spaces

In this article, by using the hybrid projection method or the shrinking projection method, we introduce two strong convergence theorems for finding a common fixed point of a finite family of sequences of nearly nonexpansive mappings in Hilbert spaces.     

渐近伪压缩和渐近非扩张映像不动点的迭代逼近问题

研究了Banach空间中渐近伪压缩和渐近非扩张映像不动点的迭代逼近问题,改进和发展了张石生教授等人的相应结果.     

非扩张映象对公共不动点的迭代逼近

对非扩张映象对引入了修改的Mann迭代格式，并证明了在一致光滑Banach空间中强收敛到其公共不动点，改进并推广了Tae—Hwa Kim and Hong—Kun Xu在2005年的结果．     

集值非扩张映象列迭代过程的收敛性及不动点

本文讨论了集值非扩张映象列的Ishikawa迭代过程的收敛性及确保迭代过程收敛到公共不动点的条件．所得结果是单值非扩张映射情形的推广和发展．     

Fixed Point Theorems and Convergence Theorems for a New Generalized Nonexpansive Mapping

Abstract

This paper introduces a new mapping that is weaker than nonexpansive mapping. The new mapping is different from the Suzuki’s generalized nonexpansive mapping. This paper introduces a new iteration process for the fixed point, and gives fixed point theorems and Convergence theorems for a new generalized nonexpansive mapping in Banach space, insteading of uniformly convex Banach space.     

Banach空间中有限个增生算子公共零点的迭代强收敛定理

令E为实自反Banach空间具一致Gteaux可微范数,AiE×E(i=1,2,…,k)为增生算子且满足∩ki=1Ai-1(0)≠φ.令C为E的非空闭凸子集并满足■C∩r>0R(I+rAi),i=1,2,…,k.将引入一种带误差项的迭代算法,并证明迭代序列强收敛于{Ai}ki=1的公共零点.     

A projection-fixed point method for a class of bilevel variational inequalities with split fixed point constraints

We propose a method for solving bilevel split variational inequalities involving strongly monotone operators in the leader problems and nonexpansive mappings in the follower ones. The proposed method is a combination between the projection method for variational inequality and the Krasnoselskii–Mann scheme for fixed points of nonexpansive mappings. Strong convergence of the iterative process is proved. Special cases are considered.     

Banach空间中渐近非扩张映射逼近序列的强收敛性

该文研究了序列{x_n}的收敛性。其中x_0∈C, x_{n+1}=α_n T^n x_n+(1-α_n)x, n=0,1,2,…,这里0≤α_n≤1，T是Banach空间中非空闭凸子集C到自身的渐近非扩张映射。同时证明了：当z_n=(1-t_n/k_n)u+t_n/k_n T^n z_n且lim_{n→∞}{(k_n-1)/(1-t_n)}=0,lim‖z_n-Tz_n‖=0时，T有不动点当且仅当{z_n}有界。这时{z_n}强收敛于T的不动点。     

Algorithms for nonexpansive self-mappings with application to the constrained multiple-set split convex feasibility fixed point problem in Hilbert spaces

In this article we devise two iteration schemes for approximating common fixed points of a finite family of nonexpansive mappings and establish the corresponding strong convergence theorem for the sequence generated by any one of our algorithms. Then we apply our results to approximate a solution of the so-called constrained multiple-set convex feasibility fixed point problem for firmly nonexpansive mappings which covers the multiple-set convex feasibility problem in the literature. In particular, our algorithms can be used to approximate the zero point problem of maximal monotone operators, and the equilibrium problem. Furthermore, the unique minimum norm solution can be obtained through our algorithms for each mentioned problem.     

Weak and Strong Convergence Theorems for New Demimetric Mappings and the Split Common Fixed Point Problem in Banach Spaces

In this paper, we consider the split common fixed point problem for new demimetric mappings in Banach spaces. Using the idea of Mann’s iteration, we prove a weak convergence theorem for finding a solution of the split common fixed point problem in Banach spaces. Furthermore, using the idea of Halpern’s iteration, we obtain a strong convergence theorem for finding a solution of the problem in Banach spaces. Using these results, we obtain well-known and new weak and strong convergence theorems in Hilbert spaces and Banach spaces.     

Convergence Theorem for Variational Inequality in Hilbert Spaces with Applications

In this paper, we study variational inequality over the set of the common fixed points of a countable family of quasi-nonexpansive mappings. To tackle this problem, we propose an algorithm and use it to prove a strong convergence theorem under suitable conditions. As applications, we study variational inequality over the solution set of different nonlinear or linear problems, like minimization problems, split feasibility problems, convexly pseudoinverse problems, convex linear inverse problems, etc.     

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.     

Banach空间中均衡问题和弱相对非扩展映射的强收敛定理及其应用(英文)

本文在Banach空间中设计了一些新的杂交迭代算法用以逼近一类均衡问题解集和弱相对非扩展映射不动点集或极大单调算子零点集的公共元.得到了一些强收敛的结论,并将它们推广到逼近一类均衡问题解集和有限个弱相对非扩展映射公共不动点集或有限个极大单调算子公共零点集的公共元的情形.最后,展示了本文的迭代算法在最优化问题上的应用.     

一类非单调二元算子方程解的Mann迭代序列的收敛性

利用Mann迭代技巧,讨论了不具有连续性和紧性条件的非单调二元算子方程解的存在唯一性,并给出了迭代序列收敛于解的误差估计,所得结果是某些已知结果本质改进和推广.     

The Equivalence of Ishikawa-Mann and Multistep Iterations in Banach Space

Let E be a real Banach space and T be a continuous Φ-strongly accretive operator. By using a new analytical method, it is proved that the convergence of Mann, Ishikawa and three-step iterations are equivalent to the convergence of multistep iteration. The results of this paper extend the results of Rhoades and Soltuz in some aspects.     

Banach空间中Mann迭代和Ishikawa迭代的等价性问题

用不同于已有的方法证明了任意实Banach空间中一致Lipschitz强连接伪压缩算子在具误差的修正的Mann迭代和具误差的修正的Ishikawa迭代下收敛和稳定的等价性,其中迭代参数{βn}仅需lim sup n→∞βn〈k/L（L＋1）,这推广和改进了目前需假设lim n→∞ βn=0和两迭代程序初始点的取值需相同条件下的已有结果.     

非扩张映射具有误差修改Ishikawa迭代算法的强收敛

在自反的Banach空间中,通过引进一个新的具有误差修改的Ishikawa迭代算法,在适当条件下,得到了关于一族非扩张映射公共不动点的强收敛定理,所获结果推广和改进了一些已知结论,最后给出了一个例子说明结果的应用.     

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.     

Banach空间中渐近非扩张非自身映射带误差Noor迭代的收敛性定理

本文主要对三个渐近非扩张非自身映射引入了一种新的投影型Noor迭代程序,并在一致凸Banach空间中给出了该Noor迭代序列的弱与强收敛性定理.我们的主要结果推广和改进了该领域许多近期的结果.