无限族严格渐近伪压缩映象隐迭代程序的强收敛定理

在Banach空间框架下,对无限族的严格渐近伪压缩映象和无限族的非扩张映象引入了一类新的隐迭代程序,并在适当的条件下,证明了该迭代程序强收敛于这两族映象的公共不动点.结果是新的,它推广和改进了一些人的最新结果.     

Convergence theorems for implicit iteration process for a finite family of continuous pseudocontractive mappings

In this paper, a necessary and sufficient conditions for the strong convergence to a common fixed point of a finite family of continuous pseudocontractive mappings are proved in an arbitrary real Banach space using an implicit iteration scheme recently introduced by Xu and Ori [H.K. Xu, R.G. Ori, An implicit iteration process for nonexpansive mappings, Numer. Fuct. Anal. Optim. 22 (2001) 767-773] in condition αn∈(0,1], and also strong and weak convergence theorem of a finite family of strictly pseudocontractive mappings of Browder-Petryshyn type is obtained. The results presented extend and improve the corresponding results of M.O. Osilike [M.O. Osilike, Implicit iteration process for common fixed points of a finite family of strictly pseudocontractive maps, J. Math. Anal. Appl. 294 (2004) 73-81].     

严格渐近伪压缩映象隐迭代序列的收敛性

含有非扩张型映射的非线性算子方程的隐式迭代法,从2001年由H.K.Xu和R.G.Ori引入以来,已有许多学者进行了研究,得出了一些有意义的成果.最近M.O.Osilike对Browder-Petyshyn意义下的严格伪压缩映象的隐迭代过程,也做出了部分研究成果,但对严格渐近伪压缩映象未曾涉及.本文将主要研究Browder-Petyshyn意义下的严格渐近伪压缩映象的隐迭代过程.并讨论它们的收敛性问题.     

严格伪压缩映像族隐格式迭代逼近不动点几何结果

对非线性算子迭代序列逼近不动点过程的几何结构进行研究,在提出并证明了一个H ilbert空间中收敛序列的钝角原理基础上,应用这个钝角原理研究了严格伪压缩映像族的隐格式迭代序列逼近公共不动点的几何结构.并证明了相应的钝角原理.这个钝角原理表述了严格伪压缩映像族的隐格式迭代序列逼近公共不动点时与公共不动点集形成了钝角关系.这个钝角关系是使用相应内积序列的上极限表示的.事实上这个钝角结果的表述形式也是一个几何变分不等式,迭代序列的极限点即是这个几何变分不等式的解.一方面这个钝角结果表述了严格伪压缩映像族公共不动点隐格式逼近的几何过程,另一方面,这个钝角结果自然是隐格式迭代序列逼近严格伪压缩映像族公共不动点的必要条件.     

Convergence of the new composite implicit iteration process with random errors

In this paper, strong convergence theorems for approximation of common fixed points of a finite family of asymptotically demicontractive mappings are proved in Banach spaces using the new composite implicit iteration scheme with errors. Our results of this paper improve and extend the corresponding results of Chen, Song, Zhou [R.D. Chen, Y.S. Song, H.Y. Zhou, Convergence theorems for implicit iteration process for a finite family of continuous pseudocontractive mappings, J. Math. Anal. Appl. 314 (2006) 701–709], Osilike [M.O. Osilike, Implicit iteration process for common fixed points of a finite family of strictly pseudocontractive maps, J. Math. Anal. Appl. 294 (2004) 73–81], Gu [F. Gu, The new composite implicit iterative process with errors for common fixed points of a finite family of strictly pseudocontractive mappings, J. Math. Anal. Appl. 329 (2007) 766–776] and Yang and Hu [L.P. Yang, G. Hu, Convergence of implicit iteration process with random errors, Acta Math. Sinica (Chin. Ser.) 51 (1) (2008) 11–22].     

φ-强伪压缩映象隐迭代过程的收敛性分析

在任意Banach空间讨论了有限个φ-强伪压缩映射族隐迭代过程的收敛性问题.利用φ的性质和迭代过程本身的特性,得到了隐迭代过程收敛于公共不动点的若干结果.这些结果补充和推广了过去的研究成果.因此它丰富和发展了隐迭代法的理论.     

Strong convergence theorems for strictly asymptotically pseudocontractive mappings in Hilbert spaces

The purpose of this paper is by using CSQ method to study the strong convergence problem of iterative sequences for a pair of strictly asymptotically pseudocontractive mappings to approximate a common fixed point in a Hilbert space. Under suitable conditions some strong convergence theorems are proved. The results presented in the paper are new which extend and improve some recent results of Acedo and Xu [Iterative methods for strict pseudo-contractions in Hilbert spaces. Nonlinear Anal., 67(7), 2258??271 (2007)], Kim and Xu [Strong convergence of modified Mann iterations for asymptotically nonexpansive mappings and semigroups. Nonlinear Anal., 64, 1140??152 (2006)], Martinez-Yanes and Xu [Strong convergence of the CQ method for fixed point iteration processes. Nonlinear Anal., 64, 2400??411 (2006)], Nakajo and Takahashi [Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups. J. Math. Anal. Appl., 279, 372??79 (2003)], Marino and Xu [Weak and strong convergence theorems for strict pseudocontractions in Hilbert spaces. J. Math. Anal. Appl., 329(1), 336??46 (2007)], Osilike et al. [Demiclosedness principle and convergence theorems for k-strictly asymptotically pseudocontractive maps. J. Math. Anal. Appl., 326, 1334??345 (2007)], Liu [Convergence theorems of the sequence of iterates for asymptotically demicontractive and hemicontractive mappings. Nonlinear Anal., 26(11), 1835??842 (1996)], Osilike et al. [Fixed points of demi-contractive mappings in arbitrary Banach spaces. Panamer Math. J., 12 (2), 77??8 (2002)], Gu [The new composite implicit iteration process with errors for common fixed points of a finite family of strictly pseudocontractive mappings. J. Math. Anal. Appl., 329, 766??76 (2007)].     

An Implicit Iteration Process with Errors for a Finite Family of r-strictly Asymptotically Pseudocontractive Mappings

In this paper,we will establish several strong convergence theorems for the approximation ofcommon fixed points of r-strictly asymptotically pseudocontractive mappings in uniformly convex Banachspaces using the modiied implicit iteration sequence with errors,and prove the necessary and sufficient conditionsfor the convergence of the sequence.Our results generalize,extend and improve the recent work,in thistopic.     

Convergence theorems of common fixed points for a finite family of Lipschitz pseudocontractions in Banach spaces

In this paper, we continue to study weak convergence problems for the implicit iteration process for a finite family of Lipschitzian continuous pseudocontractions in general Banach spaces. The results presented in this paper improve and extend the corresponding ones of Xu and Ori [H.K. Xu, R.G. Ori, An implicit iteration process for nonexpansive mappings, Numer. Funct. Anal. Optim. 22 (2001) 767–773], Osilike [M.O. Osilike, Implicit iteration process for common fixed points of a finite family of strictly pseudocontractive maps, J. Math. Anal. Appl. 294 (2004) 73–81], Chen et al. [R. Chen, Y.S. Song, H.Y. Zhou, Convergence theorems for implicit iteration process for a finite family of continuous pseudocontractive mappings, J. Math. Anal. Appl. 314 (2006) 701–709] and others.     

The new composite implicit iterative process with errors for common fixed points of a finite family of strictly pseudocontractive mappings

Convergence theorems for approximation of common fixed points of strictly pseudocontractive mappings of Browder-Petryshyn type are proved in Banach spaces using a new composite implicit iteration scheme with errors. The results presented in this paper generalize and improve the corresponding results of M.O. Osilike [M.O. Osilike, Implicit iteration process for common fixed points of a finite family of strictly pseudocontractive maps, J. Math. Anal. Appl. 294 (2004) 73-81].     

关于包含有限个强伪压缩映射的凸可行性问题解的迭代逼近

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.     

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.     

非线性映射具误差的迭代序列在Banach空间中的收敛问题

In this paper,the approximation problems of Ishikawa iteration with errors of fixedpoints for asymptotically nonexpansive mappings and asymptotically pseudocontractivemappings in arbitrary real Banach spaces are investigated. Some necessary condition andsufficient condition for the convergence of iterative sequences are given respectively. The resultsthus extend and improve some recent corresponding results.     

有限族严格伪压缩映象具误差的隐迭代序列的强收敛性

在适当的条件下,证明了有限族严格伪压缩映象具误差的隐迭代序列强收敛于其公共不动点. 所得结果改进了Osilike 与 Xu, Ori 的相应结果.     

Implicit iteration process for common fixed points of a finite family of strictly pseudocontractive maps

Convergence theorems for approximation of common fixed points of strictly pseudocontractive mappings of Browder-Petryshyn type are proved in Banach spaces using an implicit iteration scheme recently introduced by Xu and Ori [Numer. Funct. Anal. Optim. 22 (2001) 767-773].     

利普希茨伪紧缩映射下的利普希茨摄动迭代的Bruck公式

在非线性分析中,处理伪紧缩算子及其变形的解(不动点)存在性和近似性,从而使演化方程的求解已经发展成为一个独立的理论.使用近似不动点技术,采用摄动迭代方法,目的是证明利普希茨伪紧缩映射序列的收敛性.该迭代方法适用于比利普希茨伪紧缩算子更一般的非线性算子以及Bruck迭代法无法证明其收敛性的情况.推广了Chidume和Zegeye的结果.     

关于有限族Lipschitz映射多步Ishikawa迭代算法的收敛性及其应用

本文的目的是研究Lipschitz映射公共不动点问题.基于传统的Ishikawa迭代和Noor迭代方法,我们引入多步Ishikawa迭代算法,并且分别给出了该算法强收敛于有限族拟-Lipschitz映射和伪压缩映射公共不动点的充分必要条件.此外,我们证明了该算法强收敛到非扩张映射的公共不动点.作为应用,我们给出数值试验证实所得的结论.     

Strong convergence theorems for approximating common fixed points of families of nonexpansive mappings and applications

An implicit algorithm for finding common fixed points of an uncountable family of nonexpansive mappings is proposed. A new inexact iteration method is also proposed for countable family of nonexpansive mappings. Several strong convergence theorems based on our main results are established in the setting of Banach spaces. Both algorithms are applied for finding zeros of accretive operators and for solving convex minimization, split feasibility and equilibrium problems.     

凸度量空间中两无限族严格拟渐近伪压缩映象公共不动点的逼近

凸度量空间中,引入了（λ,{kn}）-严格拟渐近伪压缩映象.并且讨论了两无限族严格拟渐近伪压缩映象公共不动点的逼近问题.在适当的条件下,证明了一些强收敛定理.改进了和推广一些文献的结果.     

Approximating common fixed points of Lipschitzian pseudocontraction semigroups

In this paper, we prove a weak convergence theorem of the implicit iteration process for the semigroups of Lipschitz pseudocontractive mappings in uniformly convex Banach spaces with the Opial property.