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 of common fixed points of r-strictly asymptotically pseudocontractive mappings in uniformly convex Banach spaces using the modiied implicit iteration sequence with errors, and prove the necessary and sufficient conditions for the convergence of the sequence. Our results generalize, extend and improve the recent work, in this topic.

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）, 2258-2271 （2007）], Kim and Xu [Strong convergence of modified Mann iterations for asymptoti- cally nonexpansive mappings and semigroups. Nonlinear Anal., 64, 1140-1152 （2006）], Martinez-Yanes and Xu [Strong convergence of the CQ method for fixed point iteration processes. Nonlinear Anal., 64, 2400-2411 （2006）], Nakajo and Takahashi pings and nonexpansive semigroups. J. Math [Strong convergence theorems for nonexpansive map- Anal. Appl., 279, 372-379 （2003）], Marino and Xu [Weak and strong convergence theorems for strict pseudocontractions in Hilbert spaces. J. Math. Anal. Appl., 329（1）, 336-346 （2007）], Osilike et al. [Demiclosedness principle and convergence theorems for k-strictly asymptotically pseudocontractive maps. J. Math. Anal. Appl., 326, 1334-1345 （2007）], Liu [Convergence theorems of the sequence of iterates for asymptotically demicontractive and hemicontractive mappings. Nonlinear Anal., 26（11）, 1835-1842 （1996）], Osilike et al. [Fixed points of demi-contractive mappings in arbitrary Banach spaces. Panamer Math. J., 12（2）, 77-88 （2002）], Gu [The new composite implicit iteration process strictly pseudocontractive mappings. J. Math with errors for common fixed points of a finite family of Anal. Appl., 329, 766-776 （2007）].

关于分离变分包含和不动点问题的迭代算法（英文）

在Hilbert空间中,为了找到分离变分包含问题和渐近严格伪压缩映射不动点问题的公共解,本文介绍一种迭代算法,在某些条件下得到关于公共解的弱收敛定理.

关于压缩映射与扩张映射不动点问题的迭代算法(英文)

本文给出Hilbert空间与Banach空间中关于压缩映射、扩张映射的若干迭代格式,证明这些映射的不动点集与均衡问题解集的强(弱)收敛定理,本文改进和推广了相关文献中的结果.

广义渐近φ-半压缩映射的强收敛定理

在任意实Banach空间中,研究了依中间意义渐近k-严格伪压缩的广义渐近φ-半压缩映射带误差的修正Ishikawa迭代序列的强收敛性。所得结果改近和推广了这类问题的最新研究结果。

关于伪单调平衡问题和不动点问题的粘滞-次梯度方法

本文介绍了一个新的逼近伪单调平衡问题的解和广义渐近λ-严格伪压缩映象不动点的粘滞-次梯度方法,在Hilbert空间中建立了关于伪单调平衡问题和一簇广义渐近λ-严格伪压缩映象公共不动点的强收敛定理,并在收敛性分析中去掉了映象的一致Lipschitz连续性条件.

拟非扩张多值映像与全渐近严格伪压缩映像的分裂公共不动点问题

本在Hilbert空间中讨论了一族拟非扩张多值映像与全渐近严格伪压缩映像的分裂公共不动点问题的迭代算法,在适当的条件下证明了此迭代序列的弱收敛性和强收敛性.文中所得到的结果,推广并改进了最近一些人所发布的新结果.

Banach空间中间意义下的渐近k-严格伪压缩映象不动点的迭代逼近

设E是实Banach空间,C是E的非空闭凸子集,T:C→C是一致L-Lipschitz的中间意义下的渐近k-严格伪压缩映象且∑∞n=1γn<∞,任取一点x0∈E,{xn}是根据xn+1=(1-αn-βn)xn+αnTnxn+βnun定义的具误差的修改的Mann迭代序列,若F(T)非空有界,在对参数的一些适当限制条件下,得到了{xn}强收敛于T的一个不动点的充要条件是lim infn→∞D (xn,F(T))=0;去掉F(T)有界的条件后对参数进行同样的限制,得到了根据xn+1=(1-αn)xn+αnTnxn定义的修改的Mann迭代序列{xn}强收敛于T的一个不动点的充要条件是lim infn→∞D (xn,F(T))=0。