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1.
文章利用正规对偶映射的定义,给出了任意Banach空间Lipschitz强伪压缩映射不动点的Ishikawa迭代收敛定理.该定理不仅推广了已知结果,而且还简化了目前相应结果的证明. 相似文献
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Hilbert空间中,为了找到分离变分包含问题和demi压缩映射公共不动点集的公共解,本文介绍一种迭代算法,得到关于公共元的强收敛定理,并给出应用和数值例子. 相似文献
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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. 相似文献
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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. 相似文献
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在Banach空间中,证明了多步迭代序列强收敛于有限个强伪压缩映射的公共不动点.同时,给出了有限个(强)增生算子方程公共解的强收敛定理.所得结果推广和改进了许多重要结果. 相似文献
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本文将Hilbert空间中关于平衡与不动点问题的Halpern次外梯度算法推广到粘滞次外梯度算法,并且证明由该算法产生的迭代序列强收敛到两个集合的公共点,这两个集合分别是伪单调平衡问题的解集和一个demi-压缩映射的不动点集.我们的结果提升和统一了一些相关结论. 相似文献
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汪志明 《数学的实践与认识》2007,37(4):129-132
文章借助于对偶映射的定义,给出了任意Banach空间中LipschitzΦ-强伪压缩映射不动点的Ishikawa迭代收敛定理的简化证明,并且推广了目前相应的已知结果. 相似文献
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蒋光洁 《纯粹数学与应用数学》2010,26(5):745-750
研究Banach空间中L-Lipschitzian映射对的公共不动点逼近问题.设E表示实Banach空间,K是E中的非空闭凸子集,T,S:K→K是L-Lipschitzian映射,{xn].是带平均误差项的迭代序列,我们给出了{xn)强收敛于T和S的一个公共不动点的充分必要条件,这一结果推广了Banach空间不动点逼近定理. 相似文献
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In this paper, we introduce a modified Ishikawa iterative process for approximating a fixed point of nonexpansive mappings in Hilbert spaces. We establish some strong convergence theorems of the general iteration scheme under some mild conditions. The results improve and extend the corresponding results of many others. 相似文献
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In this work, we prove the weak and strong convergence of a sequence generated by a modified S-iteration process for finding a common fixed point of two G-nonexpansive mappings in a uniformly convex Banach space with a directed graph. We also give some numerical examples for supporting our main theorem and compare convergence rate between the studied iteration and the Ishikawa iteration. 相似文献
13.
In this paper, a kind of Ishikawa type iterative scheme with errors for approximating a common fixed point of two sequences of uniformly quasi-Lipschitzian mappings is introduced and studied in convex metric spaces. Under some suitable conditions, the convergence theorems concerned with the Ishikawa type iterative scheme with errors to approximate a common fixed point of two sequences of uniformly quasi-Lipschitzian mappings were proved in convex metric spaces. The results presented in the paper generalize and improve some recent results of Wang and Liu (C. Wang, L.W. Liu, Convergence theorems for fixed points of uniformly quasi-Lipschitzian mappings in convex metric spaces, Nonlinear Anal., TMA 70 (2009), 2067-2071). 相似文献
14.
In this paper, we introduce two modifications of the Ishikawa iteration, by using the hybrid methods, for asymptotically nonexpansive mappings and asymptotically nonexpansive semigroups in a Hilbert space. Then, we prove that such two sequences converge strongly to common fixed points of two symptotically nonexpansive mappings and asymptotically nonexpansive semigroups, respectively. Our main result is connected with the results of Plubtieng and Ungchittrakool [S. Plubtieng, K. Ungchittrakool, Strong convergence of modified Ishikawa iteration for two asymptotically nonexpansive mappings and semigroups, Nonlinear. Anal. 67(2007) 2306-2315], Martinez-Yanes and Xu [C. Martinez-Yanes, H.K. Xu, Strong convergence of CQ method for fixed point iteration processes, Nonlinear. Anal. 64 (2006) 2400-2411] and many others. 相似文献
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The purpose of this paper is to study the Ishikawa type iterative scheme to approximate a common fixed point of infinite families of uniformly quasi-Lipschitzian mappings and nonexpansive mappings in convex metric spaces. Under appropriate conditions, some convergence theorems are proved. The results presented in the paper generalize, improve and unify some recent results. 相似文献
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In this paper, we introduce an iteration scheme given by finite nonexpansive mappings in Banach spaces and then prove weak convergence theorems which are connected with the problem of image recovery. Using the results, we consider the problem of finding a common fixed point of finite nonexpansive mappings. 相似文献
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In this paper we propose a new implicit iteration scheme with perturbed mapping for approximation of common fixed points of a finite family of nonexpansive mappings. We establish some convergence theorems for this implicit iteration scheme. In particular, necessary and sufficient conditions for strong convergence of this implicit iteration scheme were obtained. 相似文献
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Paul-Emile Maingé 《Journal of Mathematical Analysis and Applications》2008,344(2):876-887
This paper deals with a general fixed point iteration for computing a point in some nonempty closed and convex solution set included in the common fixed point set of a sequence of mappings on a real Hilbert space. The proposed method combines two strategies: viscosity approximations (regularization) and inertial type extrapolation. The first strategy is known to ensure the strong convergence of some successive approximation methods, while the second one is intended to speed up the convergence process. Under classical conditions on the operators and the parameters, we prove that the sequence of iterates generated by our scheme converges strongly to the element of minimal norm in the solution set. This algorithm works, for instance, for approximating common fixed points of infinite families of demicontractive mappings, including the classes of quasi-nonexpansive operators and strictly pseudocontractive ones. 相似文献
19.
Shenghua Wang 《Journal of Computational and Applied Mathematics》2010,233(10):2620-2630
Recently, Ceng, Guu and Yao introduced an iterative scheme by viscosity-like approximation method to approximate the fixed point of nonexpansive mappings and solve some variational inequalities in Hilbert space (see Ceng et al. (2009) [9]). Takahashi and Takahashi proposed an iteration scheme to solve an equilibrium problem and approximate the fixed point of nonexpansive mapping by viscosity approximation method in Hilbert space (see Takahashi and Takahashi (2007) [12]). In this paper, we introduce an iterative scheme by viscosity approximation method for finding a common element of the set of a countable family of nonexpansive mappings and the set of an equilibrium problem in a Hilbert space. We prove the strong convergence of the proposed iteration to the unique solution of a variational inequality. 相似文献
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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. 相似文献