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1.
Banach空间中强增生算子的非线性方程的解的迭代构造 总被引:4,自引:0,他引:4
本文研究p一致光滑Banach空间X中Ishikawa迭代法.受Deng与Tan,Xu的启发,证明了,当T是从X到自身的Lipschitz强增生算子时,Ishikawa迭代法强收敛到方程Tx=f的唯一解;当T是从X的有界闭凸子集到自身的Lipschitz严格伪压缩映象时,Ishikawa迭代法强收敛到T的唯一不动点.通过去掉限制limn→∞βn=0或limn→∞αn=limn→∞βn=0,结果改进与推广了Tan,Xu的定理4.1与定理4.2,也把Deng的定理1与定理2推广到了p一致光滑Banach空间的背景. 相似文献
2.
Lipschitz局部强增殖算子的非线性方程的解的迭代构造 总被引:6,自引:2,他引:4
本文研究p一致光滑Banach空间X中Ishikawa迭代法.设T:X→K是Lipschitz局部强增殖算子,方程Tx=f的解集sol(T)非空.我们证明了sol(T)是一个单点集且Ishikawa序列强收敛到方程Tx=f的唯一解.另行,当T是从X的非空凸子集K到X的Lipschitz局部伪压缩映像且T的不动点集F(T)非空时,我们证明了F(T)是一个单点集且Ishikawa序列强收敛到T的唯一不动点.我们的结果改进和推广了[4]与[5]的结果. 相似文献
3.
Ljubomir B. Ćirić Jeong Sheok Ume Siniša N. Ješić Marina M. Arandjelović-Milovanović 《Numerical Functional Analysis & Optimization》2013,34(11-12):1231-1243
In this paper, we modify the Ishikawa iteration process and show that such process, associated with a nonlinear Lipschitzian generalized strongly pseudo-contractive operator with a fixed point in a (not necessarily uniformly smooth) Banach space, converges strongly to the unique fixed point of this operator. 相似文献
4.
本文在任意Banach空间中研究了Lipschitz φ-半压缩映象与φ-强拟增生映象的带误差项的Ishikawa迭代过程,使用新的分析技巧建立了几个强收敛定理. 相似文献
5.
一类具有广义Lipschitz条件的非线性映象的迭代过程 总被引:2,自引:0,他引:2
本文研究了广义Lipschitz强增生映象的Ishikawa型迭代和Mann型迭代过程的收敛性.所得结果统一和扩展了近期相关结果 相似文献
6.
Gu Feng 《Proceedings of the American Mathematical Society》2001,129(8):2293-2300
In this paper, the unique fixed points of multi-valued and single-valued operators of monotone type are approximated by Ishikawa and Mann iteration processes with errors in real Banach spaces. The operators may not satisfy the Lipschitzian conditions. The results presented improve and extend some recent results.
7.
Zhenyu Huang 《Journal of Mathematical Analysis and Applications》2007,329(2):935-947
In this paper, the equivalence of the strong convergence between the modified Mann and Ishikawa iterations with errors in two different schemes by Xu [Y.G. Xu, Ishikawa and Mann iteration process with errors for nonlinear strongly accretive operator equations, J. Math. Anal. Appl. 224 (1998) 91-101] and Liu [L.S. Liu, Ishikawa and Mann iterative process with errors for nonlinear strongly accretive mappings in Banach spaces, J. Math. Anal. Appl. 194 (1995) 114-125] respectively is proven for the generalized strongly successively Φ-pseudocontractive mappings without Lipschitzian assumption. Our results generalize the recent results of the papers [Zhenyu Huang, F. Bu, The equivalence between the convergence of Ishikawa and Mann iterations with errors for strongly successively pseudocontractive mappings without Lipschitzian assumption, J. Math. Anal. Appl. 325 (1) (2007) 586-594; B.E. Rhoades, S.M. Soltuz, The equivalence between the convergences of Ishikawa and Mann iterations for an asymptotically nonexpansive in the intermediate sense and strongly successively pseudocontractive maps, J. Math. Anal. Appl. 289 (2004) 266-278; B.E. Rhoades, S.M. Soltuz, The equivalence between Mann-Ishikawa iterations and multi-step iteration, Nonlinear Anal. 58 (2004) 219-228] by extending to the most general class of the generalized strongly successively Φ-pseudocontractive mappings and hence improve the corresponding results of all the references given in this paper by providing the equivalence of convergence between all of these iteration schemes for any initial points u1, x1 in uniformly smooth Banach spaces. 相似文献
8.
9.
在q(≥2)一致光滑的实Banach空间中,研究了一类非Lipschitz,非值域有界的φ-强伪压缩映射和φ-强增生映射的Ishikawa迭代收敛问题,所得结果扩展了该领域目前所有的相关结果,因而在目前更具有一般性和广泛性. 相似文献
10.
曾六川 《高校应用数学学报(英文版)》2003,18(3):283-286
Let(X,‖·‖ ) be a Banach space.Let K be a nonempty closed,convex subset of Xand T∶K→K.Assume that T is Lipschitzian,i.e.there exists L>0 such that‖ T(x) -T(y)‖≤ L‖ x -y‖for all x,y∈K.Withoutloss of generality,assume that L≥ 1 .Assume also that T is strictly pseudocontractive.According to[1 ] this may be statedas:there exists k∈ (0 ,1 ) such that‖ x -y‖≤‖ x -y + r[(I -T -k I) x -(I -T -k I) y]‖for all r>0 and all x,y∈ K.Throughout,let N denote the set of positive in… 相似文献
11.
设X是一实的Banach空间,TLX→X是—Lipschitz的增生算子;证明了具误差的Ishikawa迭代序列强收敛到x+Tx=f的唯一解;得到一个一般的收敛率估计式.进一步得到:若了T:X→X是—Lipschitz的强增生算子,则具误差的Ishikawa迭代序列强收敛到Tx=f的唯一解.文中结果推广和发展了已有的相关结果. 相似文献
12.
C. E. Chidume 《Mathematische Nachrichten》1998,189(1):49-60
Let E be a real q-uniformly smooth Banach space. Suppose T is a strongly pseudo-contractive map with open domain D(T) in E. Suppose further that T has a fixed point in D(T). Under various continuity assumptions on T it is proved that each of the Mann iteration process or the Ishikawa iteration method converges strongly to the unique fixed point of T. Related results deal with iterative solutions of nonlinear operator equations involving strongly accretive maps. Explicit error estimates are also provided. 相似文献
13.
In this paper, the equivalence of the convergence between the modified Mann–Ishikawa and multi-step Noor iterations with errors is proven for the successively strongly pseudo-contractive operators without Lipschitzian assumption. Our results generalize the recent results of the paper [B.E. Rhoades, S.M. Soltuz, The equivalence between Mann–Ishikawa iterations and multi-step iteration, Nonlinear Anal. 58 (2004) 219–228; B.E. Rhoades, S.M. Soltuz, The equivalence between the convergences of Ishikawa and Mann iterations for an asymptotically nonexpansive in the intermediate sense and strongly successively pseudo-contractive maps, J. Math. Anal. Appl. 289 (2004) 266–278] by extending to the more generalized multi-step iterations with errors and hence improve the corresponding results of all the references in bibliography by providing the equivalences of convergence between all of these up-to-date iteration schemes. 相似文献
14.
徐裕光 《数学物理学报(A辑)》2004,4(6):730-736
该文的目的是要引入比重要的 强伪压缩映象更一般的Φ 伪压缩映象,并且在更一般的假设下,用具误差的 Ishikawa和 Mann迭代过程去研究这类映象不动点的迭代逼近问题。研究结果表明:Φ 伪压缩映象T的一致连续性保证了在任意实Banach空间E中,Ishikawa迭代序列强收敛于T的唯一不动点;进一步,如果E是一致光滑的则T的连续性是不必要的 相似文献
15.
严格伪压缩映象的Ishikawa 迭代序列的收敛率估计 总被引:1,自引:0,他引:1
曾六川 《高校应用数学学报(英文版)》2002,17(2):189-192
It is shown that any fixed point of each l.ipschitzian, strictly pseudocontractive mapping 7“ on a closed convex subset K of a Banach space X may be norm approximated by Ishikawa iterative procedure. The argument in this paper provides a convergence rate estimate.Moreover the result in this paper improves, generalizes and summarizes some important and elegant recent results. 相似文献
16.
关于强增生算子的带误差项的Ishikawa和Mann迭代程序的注记 总被引:5,自引:0,他引:5
设X是实Banach空间,H:X→X是Lipschitz算子,T:X→X是值域有界且一致连续的算子,H+T是强增生算子,则具有误差项的Ishikawa和Mann迭代序列强收敛到方程Hx+Tx=f的唯一解,这些结论推广了最新文献中的相应结果。 相似文献
17.
姚新颉 《应用数学与计算数学学报》2004,18(1):67-70
本文证明了定义在Banach空间X中闭凸子集K上的Lipschitz严格伪压缩 映射T的不动点,可由Ishilkawa迭代程序逼近,并给出了更一般的收敛率的估计,从而 统一和发展了近期的一些有关的结果. 相似文献
18.
谷峰 《数学的实践与认识》2009,39(2)
设X为赋范线性空间,K为X的非空凸子集,T:K→K为LipschitzΦ-半压缩映象.设{αn}n∞=0和{βn}n∞=0为[0,1]中的实数列且满足一定条件.则Ishikawa迭代序列{xn}n∞=0强收敛于T的唯一不动点.结果完整地回答了周海云提出的公开问题. 相似文献
19.
赋范空间中渐近伪压缩映象不动点的迭代逼近 总被引:1,自引:0,他引:1
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. 相似文献
20.
关于Ishikawa迭代程序逼近严格伪压缩映象的不动点问题 总被引:6,自引:0,他引:6
设X是一Banach空间,K是X的闭凸子集,T:K→K是严格伪压缩的Lipschitz映象。我们证明了T的任何不动点可用Ishikawa迭代程序来范数逼近,并提供了收敛率的估计。本文结果在一定程序上推广与概括了Sastry与Babu[2]的定理1,在一定程度上改进与推广了Liu[1]的定理1与定理2。 相似文献