共查询到20条相似文献,搜索用时 15 毫秒
1.
关于强伪压缩映射迭代程序的稳定性 总被引:2,自引:0,他引:2
设E是具有一致凸对偶E^*的实Banach空间,E^*是凸性模满足:δE*(ε)≥cε^q,其中q≥2和c≥0是常数。在E中,我们研究没有连续性假设的强伪压缩映射的广义Mann和广义Ishikawa迭代程序的稳定性。 相似文献
2.
本文结果表征了用于构造强增生算子方程解,m-增生算子方程解及强伪压缩算子不动点的(带误差的)Ishikawa型迭代序列的收敛性,推广与改进了Chidume与Osilike的定理1,定理2及定理3(Nonlinear Anal.TMA,1999,36(7):863-872)。 相似文献
3.
Andrei Sipoş 《Numerical Functional Analysis & Optimization》2017,38(1):80-90
We show that a variant of a previously defined function can be used to characterize 2-uniform smoothness. We then obtain greatly simplified proofs of two convergence theorems in the literature using a generalization of a lemma of and the aforementioned characterization. We also more easily obtain rates of asymptotic regularity corresponding to the studied iterations. Finally, we derive a way to relate two constants which are characteristic to 2-uniformly smooth spaces. 相似文献
4.
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
5.
Luchuan Zeng 《高等学校计算数学学报(英文版)》2006,15(1):31-39
Let 1<ρ≤2,E be a real ρ-uniformly smooth Banach space and T:E→E be a continuous and strongly accretive operator.The purpose of this paper is to investigate the problem of approximating solutions to the equation Tx=f by the Ishikawa iteration procedure with errors (?) where x_0 ∈ E,{u_n},{υ_n}are bounded sequences in E and{α_n},{b_n},{c_n},{a_n~'},{b_n~'},{c_n~'} are real sequences in[0,1].Under the assumption of the condition 0<α≤b_n c_n,An≥0, it is shown that the iterative sequence{x_n}converges strongly to the unique solution of the equation Tx=f.Furthermore,under no assumption of the condition(?)(b_n~' c_n~')=0,it is also shown that{x_n}converges strongly to the unique solution of Tx=f. 相似文献
6.
强伪压缩算子带误差的Ishikawa迭代的强稳定性 总被引:2,自引:0,他引:2
设X是任意实Banach空间,T:X→X是一Lipschitz强伪压缩算子,本给出T带误差的Ishikawa迭代过程的强稳定性,并给出一个涉及Lipschitz强增生算子T的非线性方程Tx=f迭代解的强稳定性。 相似文献
7.
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
8.
9.
LetXbearealBanachspacewithdualitymappingJ:X→ 2 X givenbyJ(x) =j∈X :(x ,j) =x 2 =j 2 ,whereX denotesthedualspaceofX .AnoperatorT :D(T) X→Xiscalledstronglyaccretiveifforanyx ,y∈D(T)thereexistsj(x -y)∈J(x -y)andaconstantk >0suchthat(Tx-Ty,j(x-y) ) ≥k x-y 2 .Withoutlossofgenerality ,it… 相似文献
10.
Ke Su 《应用数学学报(英文版)》2005,21(4):565-570
In this paper, we suggest and analyse a three-step iterative scheme with errors for solving nonlinear strongly accretive operator equation Tx = f without the Lipshitz condition. The results presented in this paper improve and extend current results in the more general setting. 相似文献
11.
曾六川 《数学物理学报(A辑)》2004,4(6):654-660
该文在Banach空间中证明了,带误差的Ishikawa迭代序列强收敛到Lipschitz连续的增生算子方程的唯一解.而且,也给Ishikawa迭代序列提供了一般的收敛率估计.利用该结果还推得,带误差的Ishikawa迭代序列也强收敛到Lipschitz连续的强增生算子方程的唯一解. 相似文献
12.
Lipschitz强增生算子方程逼近解的带误差的Ishikawa迭代程序 总被引:2,自引:0,他引:2
曾六川 《应用泛函分析学报》2002,4(3):274-279
设E是任意实Banach空间,T:E→E是Ligpschitz的强增生算子。证明了带误差的Ishikawa迭代序列强收敛到方程Tx=f的唯一解。特别地,还给出了Ishikawa迭代序列的收敛率估计。另一方面,一个相关结果,讨论了E中Lipschitz强伪压缩映象的不动点的带误差的Ishikawa迭代序列的收敛性。 相似文献
13.
Sascha Trostorff 《PAMM》2014,14(1):983-984
An abstract notion of exponential stability within the framework of evolutionary equations is provided. Sufficient conditions for the exponential stability are given in terms of the so-called material-law operator, which is defined via an operator-valued analytic function. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
14.
Dagang Tian 《偏微分方程(英文版)》1995,8(2):108-114
A class of strongly coupled semilinear reaction-diffusion equations is discussed. The FitzHugh-Nagumo equation in [1] is only an example. The results that strongly coupled term generates an analytic semigroup extended the results in [4]. The results of the existence and uniqueness of solution and the stability of zero solution improved that in [1]. This paper also discusses the existence of periodic solution. 相似文献
15.
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
16.
《Journal of Mathematical Analysis and Applications》1997,213(1):296-307
LetEbe a real Banach space with a uniformly convex dual spaceE*. SupposeT:E → Eis a continuous (not necessarily Lipschitzian) strongly accretive map such that (I − T) has bounded range, whereIdenotes the identity operator. It is proved that the Ishikawa iterative sequence converges strongly to the unique solution of equationTx = f,f ∈ E. Our results extend and complement the recent results obtained by Chidume. 相似文献
17.
关于Banach空间中增生算子方程的迭代法收敛率估计 总被引:1,自引:0,他引:1
本文研究Banach空间中增生算子方程的Ishikawa迭代法收敛率估计。本文所得结果在以下方面改进和推广了刘理蔚的结果(Nonlinear Anal.42(2)(2000),271-276):(1)以假设{αn},{βn}在不同区间上独立取值代替刘的假设limn→∞αn=limn→∞βn=0;(2)以一般的收敛率估计和几何收敛率估计代替刘的收敛率估计||xm=x^*||=O(1/m)。 相似文献
18.
Banach空间中含强增生算子的非线性方程的迭代解 总被引:7,自引:2,他引:7
设X为实Banach空间,X*为其一致凸的共轭空间.设T:X→X为Lipschitzian强增生映象,L≥1为其Lipschitzian常数,k∈(0,1)为其强增生常数.设{αn},{βn}为[0,1]中的两个实数列满足:(ⅰ)αn→0(n→∞);(ⅱ)βn<L(1+L)/k(1-k)(n≥0);(ⅲ).假设为X中两序列满足:=o(βn)与μn→0(n→∞).任取x0∈X,则由(IS)1xn+1=(1-αn)xn+αnSyn+unyn=(1-βn)xn+βnSxn+μn(n≥0){所定义的迭代序列{xn强收敛于方程T 相似文献
19.
Le Van Hien 《Ukrainian Mathematical Journal》2005,57(7):1066-1076
We study the stability of solutions of fuzzy differential equations by Lyapunov's second method. By using scale equations
and the comparison principle for Lyapunov-like functions, we give sufficient criteria for the stability and asymptotic stability
of solutions of fuzzy differential equations.
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Published in Ukrains'kyi Matematychnyi Zhurnal, Vol. 57, No. 7, pp. 904–911, July, 2005. 相似文献
20.
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