Common fixed points of new iterations for two asymptotically nonexpansive nonself-mappings in a Banach space

In this paper, we introduce a new two-step iterative scheme for two asymptotically nonexpansive nonself-mappings in a uniformly convex Banach space. Weak and strong convergence theorems are established for the new two-step iterative scheme in a uniformly convex Banach space.     

New iterative schemes for asymptotically quasi-nonexpansive nonself-mappings in Banach spaces

In this paper, a new two-step iterative scheme with errors is introduced for two asymptotically quasi-nonexpansive nonself-mappings. Several convergence theorems are established in real Banach spaces and real uniformly convex Banach spaces. Our theorems improve and extend the results due to Thianwan [S. Thianwan, Common fixed point of new iterations for two asymptotically nonexpansive nonself-mappings in a Banach space, J. Comput. Appl. Math. 224 (2009) 685-695] and many other papers.     

Fixed-Point Iterations for Asymptotically Nonexpansive Mappings in Banach Spaces

In this paper, we suggest and analyze a three-step iterative scheme for asymptotically nonexpansive mappings in Banach spaces. The new iterative scheme includes Ishikawa-type and Mann-type interations as special cases. The results obtained in this paper represent an extension as well as refinement of previous known results.     

Banach空间中渐近非扩张非自身映射带误差Noor迭代的收敛性定理

本文主要对三个渐近非扩张非自身映射引入了一种新的投影型Noor迭代程序,并在一致凸Banach空间中给出了该Noor迭代序列的弱与强收敛性定理.我们的主要结果推广和改进了该领域许多近期的结果.     

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.     

On the convergence of modified Noor iterations with errors for asymptotically nonexpansive mappings

In this paper, several weak and strong convergence theorems are established for a modified Noor iterative scheme with errors for three asymptotically nonexpansive mappings in Banach spaces. Mann-type, Ishikawa-type, and Noor-type iterations are covered by the new iteration scheme. Our results extend and improve the recently announced ones [B.L. Xu, M.A. Noor, Fixed point iterations for asymptotically nonexpansive mappings in Banach spaces, J. Math. Anal. Appl. 267 (2002) 444-453; Y.J. Cho, H. Zhou, G. Guo, Weak and strong convergence theorems for three-step iterations with errors for asymptotically nonexpansive mappings, Comput. Math. Appl. 47 (2004) 707-717] and many others.     

Strong convergence theorems for multi-step Noor iterations with errors in Banach spaces

In this paper, we established two strong convergence theorems for a multi-step Noor iterative scheme with errors for mappings of asymptotically nonexpansive in the intermediate sense(asymptotically quasi-nonexpansive, respectively) in Banach spaces. Our results extend and improve the recent ones announced by Xu and Noor [B.L. Xu, M.A. Noor, Fixed-point iterations for asymptotically nonexpansive mappings in Banach spaces, J. Math. Anal. Appl. 267 (2002) 444-453], Cho, Zhou and Guo [Y.J. Cho, H. Zhou, G. Guo, Weak and strong convergence theorems for three-step iterations with errors for asymptotically nonexpansive mappings, Comput. Math. Appl. 47 (2004) 707-717], and many others.     

Convergence theorems for a new iteration scheme for mixed-type asymptotically nonexpansive mappings

In this paper, we introduce a new iteration scheme of mixed type for two asymptotically nonexpansive self-mappings and two asymptotically nonexpansive nonself-mappings, and prove some weak and strong convergence theorems of the proposed iteration scheme in uniformly convex Banach spaces. Our results improve and extend the corresponding results given by some authors.     

迭代(L-α)一致李普希兹渐近非扩张映射的不动点迭代

首先定义一致凸Banach空间某非空紧子集上的一种新的映射—(L-α)一致李普希兹渐近非扩张映射,在该子集上构造关于(L-α)一致李普希兹渐近非扩张映射的三步迭代序列,然后来讨论三步迭代序列的收敛性。     

渐进非扩张非自映像新的迭代的强收敛

研究了渐进非扩张非自映像新的迭代的强收敛问题.利用保核收缩映像的基本性质,定义了一种新的Ishikawa型迭代序列,并在一致凸的Banach空间里,证明了该迭代序列在适当条件下强收敛到T的不动点.结果改进和推广了一些最新成果.     

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.     

Implicit iterative algorithms for asymptotically nonexpansive mappings in the intermediate sense and Lipschitz-continuous monotone mappings

In this paper, we introduce some implicit iterative algorithms for finding a common element of the set of fixed points of an asymptotically nonexpansive mapping in the intermediate sense and the set of solutions of the variational inequality problem for a monotone, Lipschitz-continuous mapping. These implicit iterative algorithms are based on two well-known methods: extragradient and approximate proximal methods. We obtain some weak convergence theorems for these implicit iterative algorithms. Based on these theorems, we also construct some implicit iterative processes for finding a common fixed point of two mappings, such that one of these two mappings is taken from the more general class of Lipschitz pseudocontractive mappings and the other mapping is asymptotically nonexpansive.     

Banach空间中依中间意义渐近非扩张映象具误差的三步平均值迭代序列收敛问题

研究了Banach空间中依中间意义渐近非扩张映象具误差的三步平均值迭代序列收敛问题,所得结果改进和发展了相关文献中的结果.     

非扩张半群的变分不等式的不动点解的粘性逼近方法

本文研究了非扩张半群的变分不等式的不动点解的迭代算法.利用变分不等式与不动点问题的解的关系,结合粘性逼近方法,建立了非扩张半群的不动点的两步迭代格式,证明了该方法所得到的迭代序列在一定条件下的强收敛性,并收敛于某变分不等式的唯一解.     

Banach空间中严格渐近伪压缩映象的收敛性问题

在一致凸的Banach空间中，采用新的证明方法研究了严格渐近伪压缩映象和渐近非膨胀映象带误差的修正的Mann和Ishikawa迭代程序的收敛性问题，不要求定义域、值域有界，且迭代系数更简单．     

Banach空间中渐近非扩张强连续半群不动点的粘性逼近

在具有一致Gateaux可微范数的Banach空间中,讨论了一个逼近渐近非扩张强连续半群不动点的两步粘性逼近方法,并在一定条件下证明了该方法所得到的迭代序列的强收敛性.     

与渐近非扩张半群不动点问题相关的分裂等式混合均衡问题及其应用

研究了与渐近非扩张半群不动点问题相关的分裂等式混合均衡问题.在等式约束下,为同时逼近两个空间中混合均衡问题和渐近非扩张半群不动点问题的公共解,借助收缩投影方法引出了一种迭代程序.在适当条件下,该迭代算法的强收敛性被证明.文末还把所得结果应用于分裂等式混合变分不等式问题和分裂等式凸极小化问题.     

Approximating solutions of variational inequalities for asymptotically nonexpansive mappings

By using viscosity approximation methods for asymptotically nonexpansive mappings in Banach spaces, some sufficient and necessary conditions for a new type of iterative sequences to converging to a fixed point which is also the unique solution of some variational inequalities are obtained. The results presented in the paper extend and improve some recent results in [C.E. Chidume, Jinlu Li, A. Udomene, Convergence of paths and approximation of fixed points of asymptotically nonexpansive mappings, Proc. Amer. Math. Soc. 138 (2) (2005) 473-480; N. Shahzad, A. Udomene, Fixed point solutions of variational inequalities for asymptotically nonexpansive mappings in Banach spaces, Nonlinear Anal. 64 (2006) 558-567; T.C. Lim, H.K. Xu, Fixed point theories for asymptotically nonexpansive mappings, Nonlinear Anal. TMA, 22 (1994) 1345-1355; H.K. Xu, Viscosity approximation methods for nonexpansive mappings, J. Math. Anal. Appl., 298 (2004) 279-291].     

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.     

集值渐近拟非扩张映射的不动点收敛定理

研究一致凸Banach空间中集值渐近拟非扩张映射的关于有限步迭代序列逼近公共不动点的充分必要条件,并在此条件下,证明了该序列收敛到公共不动点的一些强收敛定理,所得结果是单值映射情形的推广和发展.