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.     

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.     

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．     

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.     

三个渐进非扩张映象对公共不动点的逼近问题

研究Banach空间中三个渐进非扩张映象对公共不动点的逼近问题.本文结果发展和改进了最近一些人的最新结果.     

逼近一致凸Banach空间中渐近非扩张映象的不动点

借助于B ruck′s不等式,研究了一致凸Banach空间中渐近非扩张映象不动点的具误差的Ish ikaw a迭代序列的强收敛定理.所得的结果推广和改进了Schu,Rhoades,周海云,王绍荣等作者的相应结果.     

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．     

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].     

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: