共查询到20条相似文献,搜索用时 987 毫秒
1.
A new iteration process is introduced and proved to converge strongly to a common fixed point for a finite family of generalized Lipschitz nonlinear mappings in a real reflexive Banach space E with a uniformly Gâteaux differentiable norm if at least one member of the family is pseudo-contractive. It is also proved that a slight modification of the process converges to a common zero for a finite family of generalized Lipschitz accretive operators defined on E. Results for nonexpansive families are obtained as easy corollaries. Finally, the new iteration process and the method of proof are of independent interest. 相似文献
2.
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
3.
Let E be a 2-uniformly real Banach space and F,K:E→E be nonlinear-bounded accretive operators. Assume that the Hammerstein equation u+KFu=0 has a solution. A new explicit iteration sequence is introduced and strong convergence of the sequence to a solution of the Hammerstein equation is proved. The operators F and K are not required to satisfy the so-called range condition. No invertibility assumption is imposed on the operator K and F is not restricted to be an angle-bounded (necessarily linear) operator. 相似文献
4.
R.R Phelps 《Journal of Functional Analysis》1974,17(1):78-90
It is shown that a Banach space E has the Radon-Nikodym property (equivalently, every bounded subset of E is dentable) if and only if every bounded closed convex subset of E is the closed convex hull of its strongly exposed points. Using recent work of Namioka, some analogous results are obtained concerning weak1 strongly exposed points of weak1 compact convex subsets of certain dual Banach spaces. 相似文献
5.
We obtain a covering theorem for E ?-dense E-semigroups showing that such a semigroup has an E ?-dense, strongly E ?-unitary E-semigroup as a cover and describe the structure of the latter semigroups. 相似文献
6.
《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
7.
Xiao-shan Chen 《高校应用数学学报(英文版)》2013,28(3):303-310
A complex, square matrix E is called coninvolutory if EE = I, where E denotes complex conjugate of the matrix E and I is an identity matrix. In this paper we introduce the coninvolutory decomposition of a complex matrix and investigate a Newton iteration for computing the coninvolutory factor. A simple numerical example illustrates our results. 相似文献
8.
We prove that if E is a rearrangement-invariant space, then a boundedly complete basis exists in E, if and only if one of the following conditions holds: 1) E is maximal and E ≠ L 1[0, 1]; 2) a certain (any) orthonormal system of functions from L ∞[0, 1], possessing the properties of the Schauder basis for the space of continuous on [0, 1] functions with the norm L ∞, represents a boundedly complete basis in E. As a corollary, we state the following assertion: Any (certain) orthonormal system of functions from L ∞[0, 1], possessing the properties of the Schauder basis for the space of continuous on [0, 1] functions with the norm L ∞, represents a spanning basis in a separable rearrangement-invariant space E, if and only if the adjoint space E* is separable. We prove that in any separable rearrangement-invariant space E the Haar system either forms an unconditional basis, or a strongly conditional one. The Haar system represents a strongly conditional basis in a separable rearrangement-invariant space, if and only if at least one of the Boyd indices of this space is trivial. 相似文献
9.
Ian H Sloan E Noussair B.J Burn 《Journal of Mathematical Analysis and Applications》1979,69(1):84-103
A class of projection methods, differing from the classical projection methods, is studied for the equation y = f + Ky, where K is a compact linear operator in a Banach space E, and f?E, In these methods K is approximated by a finite-rank operator Kn, which is constructed with the aid of certain projection operators, and which satisfies Knz = Kz for all z belonging to a chosen subspace Un ? E. Under certain conditions, it is shown that the convergence of the approximate solution is faster than that of any classical projection method based on the subspace Un. In an example, Un is taken to consist of piecewise constant functions, and the projections are so chosen that the method becomes equivalent to a single iteration of a classical method, the collocation method; in this case the error (in the supremum norm) is , compared with for the collocation method. 相似文献
10.
《Journal of Computational and Applied Mathematics》2002,149(1):251-265
The approximate solutions in standard iteration methods for linear systems Ax=b, with A an n by n nonsingular matrix, form a subspace. In this subspace, one may try to construct better approximations for the solution x. This is the idea behind Krylov subspace methods. It has led to very powerful and efficient methods such as conjugate gradients, GMRES, and Bi-CGSTAB. We will give an overview of these methods and we will discuss some relevant properties from the user's perspective view.The convergence of Krylov subspace methods depends strongly on the eigenvalue distribution of A, and on the angles between eigenvectors of A. Preconditioning is a popular technique to obtain a better behaved linear system. We will briefly discuss some modern developments in preconditioning, in particular parallel preconditioners will be highlighted: reordering techniques for incomplete decompositions, domain decomposition approaches, and sparsified Schur complements. 相似文献
11.
Let E be a real Banach space, K a closed convex nonempty subset of E. Let be m total asymptotically nonexpansive mappings. An iterative sequence for approximation of common fixed points (assuming existence) of T1,T2,…,Tm is constructed; necessary and sufficient conditions for the convergence of the scheme to a common fixed point of the mappings are given. Furthermore, in the case that E is uniformly convex, a sufficient condition for convergence of the iteration process to a common fixed point of mappings under our setting is established. 相似文献
12.
Let X be an irreducible smooth projective curve over an algebraically closed field k of positive characteristic and G a simple linear algebraic group over k. Fix a proper parabolic subgroup P of G and a nontrivial anti-dominant character λ of P. Given a principal G-bundle EG over X, let EG(λ) be the line bundle over EG/P associated to the principal P-bundle EG→EG/P for the character λ. We prove that EG is strongly semistable if and only if the line bundle EG(λ) is numerically effective. For any connected reductive algebraic group H over k, a similar criterion is proved for strongly semistable H-bundles. 相似文献
13.
Accelerated modulus-based matrix splitting iteration methods for linear complementarity problem 总被引:1,自引:0,他引:1
For the large sparse linear complementarity problem, a class of accelerated modulus-based matrix splitting iteration methods is established by reformulating it as a general implicit fixed-point equation, which covers the known modulus-based matrix splitting iteration methods. The convergence conditions are presented when the system matrix is either a positive definite matrix or an H +-matrix. Numerical experiments further show that the proposed methods are efficient and accelerate the convergence performance of the modulus-based matrix splitting iteration methods with less iteration steps and CPU time. 相似文献
14.
Philippe Galinier 《Discrete Applied Mathematics》2008,156(2):267-279
Let G=(V,E) be a graph with vertex set V and edge set E. The k-coloring problem is to assign a color (a number chosen in {1,…,k}) to each vertex of G so that no edge has both endpoints with the same color. The adaptive memory algorithm is a hybrid evolutionary heuristic that uses a central memory. At each iteration, the information contained in the central memory is used for producing an offspring solution which is then possibly improved using a local search algorithm. The so obtained solution is finally used to update the central memory. We describe in this paper an adaptive memory algorithm for the k-coloring problem. Computational experiments give evidence that this new algorithm is competitive with, and simpler and more flexible than, the best known graph coloring algorithms. 相似文献
15.
Xiao-Guang Lv T.Z. HuangLiang Li 《Journal of Computational and Applied Mathematics》2011,235(9):3112-3114
In [1], Gu and Tian [Chuanqing Gu, Zhaolu Tian, On the HSS iteration methods for positive definite Toeplitz linear systems, J. Comput. Appl. Math. 224 (2009) 709-718] proposed the special HSS iteration methods for positive definite linear systems Ax=b with A∈Cn×n a complex Toeplitz matrix. But we find that the special HSS iteration methods are incorrect. Some examples are given in our paper. 相似文献
16.
Ivan Kolá? 《Czechoslovak Mathematical Journal》2012,62(2):487-494
We characterize Weilian prolongations of natural bundles from the viewpoint of certain recent general results. First we describe the iteration F(EM) of two natural bundles E and F. Then we discuss the Weilian prolongation of an arbitrary associated bundle. These two auxiliary results enables us to solve our original problem. 相似文献
17.
Jordi Juan-Huguet 《Monatshefte für Mathematik》2011,164(4):427-437
It is proved that every weakly non-quasianalytic ultradifferentiable curve with values in a Fréchet space E is topologically (or strongly) ultradifferentiable if and only if the space E satisfies the topological invariant (DN), thus solving a problem posed by Kriegl and Michor. 相似文献
18.
Zhonghao Jiang 《Semigroup Forum》2003,67(1):50-62
We introduce a class of strongly E *-unitary inverse semigroups S i (G, P) (i = 1,2) determined by a group G and a submonoid P of G and give an embedding theorem for S i (G, P). Moreover we characterize 0-bisimple strongly E *-unitary inverse monoids and 0-bisimple strongly F *-inverse monoids by using S i (G, P). 相似文献
19.
Henryk Hudzik 《Indagationes Mathematicae》2006,17(3):373-395
General results saying that a point x of the unit sphere S(E) of a Köthe space E is an extreme point (a strongly extreme point) [an SU-point] of B(E) if and only if ‖x‖ is an extreme point (a strongly extreme point) [an SU-point] of B(E+) and ‖x‖ is a UM-point (a ULUM-point) [nothing more] of E are proved. These results are applied to get criteria for extreme points and SU-points of the unit ball in Caldern-Lozanovski spaces which refer to problem XII from [5]. Strongly extreme points in these spaces are also discussed. 相似文献
20.
Liping Yang Xiangsheng Xie Shiguo Peng 《Journal of Applied Mathematics and Computing》2009,31(1-2):81-95
Let E be a real uniformly convex and smooth Banach space with P as a sunny nonexpansive retraction, K be a nonempty closed convex subset of E. Let {S i } i=1 N , {T i } i=1 N :K→K be two finite families of weakly inward and asymptotically nonexpansive mappings with respect to P. It is proved that the composite implicit iteration process converges weakly and strongly to a common fixed point of {S i } i=1 N , {T i } i=1 N under certain conditions. The results of this paper improve and extend some well known corresponding results. 相似文献