渐近拟非扩张型映象的Ishikawa迭代序列的强收敛性

通过引入一新型条件,研究了渐近拟非扩张型映象不动点的具误差的修正的Ish ikaw a迭代序列的迭代逼近问题,得到新的结果.     

关于渐近伪压缩型映象的不动点的迭代构造

本文引入了Banach空间中一类渐近伪压缩型映象,它概括了熟知的若干映象类成特例.而且,还研究了关于这类映象的带误差的修改了的Ishikawa与Mann迭代序列的逼近问题.本文所得结果改进与推广了张石生教授的所有结果以及前人研究的相应结果.     

Iterative sequences with mixed errors for asymptotically quasi-nonexpansive type mappings in Banach spaces

The purpose of this paper is to study necessary and sufficient conditions for the Ishikawa iterative sequence with mixed errors of asymptotically quasi-nonexpansive type mappings in Banach spaces to converge to a fixed point in Banach spaces. The results presented in this paper complememt, improve and prefect the corresponding results of [1]–[4] and [7]–[9]. This revised version was published online in June 2006 with corrections to the Cover Date.     

赋范空间中渐近伪压缩映象不动点的迭代逼近

设x是赋范线性空间，D是x的非空子集．设T：D→x是一个一致L—Lipschitz的渐近伪压缩映象，F(T)表T的不动点集且F(T)非空．在迭代参数(αn)和(βn)的适当假设下，证明了修改了的具有误差项的Ishikawa和Mann迭代过程强收敛于T的不动点q．几个相关结果处理赋范空间中渐近非扩张映象不动点的迭代逼近问题．所得结果改进和推广了Chang，Park和Cho，Geobel和Kirl，Liu以及Schu等人的相关结果．     

关于渐近拟非扩展型映象不动点的迭代逼近问题

在新型条件下研究了Banach空间中渐近拟非扩展型映象不动点的迭代逼近问题;所得结果补充和推广了文[1-3]等人的相应成果.     

On the convergence of implicit iteration process with error for a finite family of asymptotically nonexpansive mappings

The purpose of this paper is to study the weak and strong convergence of implicit iteration process with errors to a common fixed point for a finite family of asymptotically nonexpansive mappings and nonexpansive mappings in Banach spaces. The results presented in this paper extend and improve the corresponding results of [H. Bauschke, The approximation of fixed points of compositions of nonexpansive mappings in Hilbert space, J. Math. Anal. Appl. 202 (1996) 150-159; B. Halpern, Fixed points of nonexpansive maps, Bull. Amer. Math. Soc. 73 (1967) 957-961; P.L. Lions, Approximation de points fixes de contractions, C. R. Acad. Sci. Paris, Ser. A 284 (1977), 1357-1359; S. Reich, Strong convergence theorems for resolvents of accretive operators in Banach spaces, J. Math. Anal. Appl. 75 (1980) 287-292; Z.H. Sun, Strong convergence of an implicit iteration process for a finite family of asymptotically quasi-nonexpansive mappings, J. Math. Anal. Appl. 286 (2003) 351-358; R. Wittmann, Approximation of fixed points of nonexpansive mappings, Arch. Math. 58 (1992) 486-491; H.K. Xu, M.G. Ori, An implicit iterative process for nonexpansive mappings, Numer. Funct. Anal. Optimiz. 22 (2001) 767-773; Y.Y. Zhou, S.S. Chang, Convergence of implicit iterative process for a finite family of asymptotically nonexpansive mappings in Banach spaces, Numer. Funct. Anal. Optimiz. 23 (2002) 911-921].     

Banach空间中几乎渐近非扩张型映象的不动点的迭代逼近

在Banach空间中引入了一类新的几乎渐近非扩张型映象,概括了Banach空间中若干熟知的非线性的Lipschitz映象类与非Lipschitz映象类成特例;例如,熟知的非扩张映象类,渐近非扩张映象类与渐近非扩张型映象类.考虑了用于逼近几乎渐近非扩张型映象不动点的带误差的修改了的Ishikawa迭代序列的收敛性问题.关于Banach空间范数的S.S.Chang的不等式与H.K.Xu的不等式皆被用于做精确不动点与近似不动点间的误差估计.而且,张石生教授用于做带误差的修改了的Ishikawa迭代序列收敛性分析的方法(应用数学和力学,2001,22(1):23-31)被推广到几乎渐近非扩张型映象的情况.给出了用于求一致凸Banach空间中几乎渐近非扩张型映象不动点的带误差的修改了的Ishikawa迭代序列的新的收敛判据.并且,由该判据,立即得到了此类映象的带误差的修改了的Mann迭代序列的新的收敛判据.上述结果统一、改进与推广了张石生教授关于用带误差的修改了的Ishikawa与Mann迭代序列来逼近渐近非扩张型映象不动点方面的结果.     

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.     

An ergodic theorem for asymptotically nonexpansive mappings in the intermediate sense

This paper is concerned with an ergodic theorem for asymptotically nonexpansive mappings in the intermediate sense in Banach spaces.

     

Banach空间中有限个渐近非扩展映象公共不动点的隐式迭代逼近

在更一般的条件下研究了Banach空间中有限个渐近非扩展映象和非扩展映象公共不动点的隐式迭代过程的强收敛问题．所得结果推广和发展了已有文献中的有关结果．     

“渐近非扩张映象不动点具误差的迭代逼近”的注记

本文在去掉条件"T在D上一致渐近正则"的情况下,在一致凸Banach空间中给出了几个渐近拟非扩张型映象和渐近非扩张型映象不动点的迭代逼近定理.这些定理推广和发展了最近一些文献的相关成果,并且改进了定理的证明方法.     

A fixed-point theorem for asymptotically contractive mappings

We present fixed point theorems for a nonexpansive mapping from a closed convex subset of a uniformly convex Banach space into itself under some asymptotic contraction assumptions. They generalize results valid for bounded convex sets or asymptotically compact sets.

     

Banach空间中渐近非扩张映象不动点的迭代逼近问题

本文研究Banach空间中渐近非扩张映象和渐近伪压缩映象不动点的迭代逼近问题,本文结果是[4,5,7]中相应结果的发展和改进。     

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)].     

Convergence analysis of implicit iterative algorithms for asymptotically nonexpansive mappings

In this paper, we consider the weak and strong convergence of an implicit iterative process with errors for two finite families of asymptotically nonexpansive mappings in the framework of Banach spaces. Our results presented in this paper improve and extend the recent ones announced by many others.     

Weak and strong convergence of the Ishikawa iterative process for a finite family of asymptotically nonexpansive mappings

In this paper, we introduce an Ishikawa implicit iterative process with errors for a finite family of N asymptotically nonexpansive mappings as follows:

     

Banach空间中几乎渐近非扩张型映象具混合误差的迭代程序

研究了Banach空间中几乎渐近非扩张型映象不动点的迭代逼近问题,所得结果发展和改进了张石生教授,曾六川教授等人的一些最新成果.     

On asymptotically nonexpansive mappings in hyperconvex metric spaces

Since bounded hyperconvex metric spaces have the fixed point property for nonexpansive mappings, it is natural to extend such a powerful result to asymptotically nonexpansive mappings. Our main result states that the approximate fixed point property holds in this case. The proof is based on the use, for the first time, of the ultrapower of a metric space.

     

Geometrical coefficients and the structure of the fixed-point set of asymptotically regular mappings in Banach spaces

It is shown that if E is a separable and uniformly convex Banach space with Opial’s property and C is a nonempty bounded closed convex subset of E, then for some asymptotically regular self-mappings of C the set of fixed points is not only connected but even a retract of C. Our results qualitatively complement, in the case of a uniformly convex Banach space, a corresponding result presented in [T. Domínguez, M.A. Japón, G. López, Metric fixed point results concerning measures of noncompactness mappings, in: W.A. Kirk, B. Sims (Eds.), Handbook of Metric Fixed Point Theory, Kluwer Acad. Publishers, Dordrecht, 2001, pp. 239-268].     

Structure of the fixed point set and common fixed points of asymptotically nonexpansive mappings

Let be a Banach space, a weakly compact convex subset of and an asymptotically nonexpansive mapping. Under the usual assumptions on which assure the existence of fixed point for , we prove that the set of fixed points is a nonexpansive retract of . We use this result to prove that all known theorems about existence of fixed point for asymptotically nonexpansive mappings can be extended to obtain a common fixed point for a commuting family of mappings. We also derive some results about convergence of iterates.