排序方式: 共有210条查询结果,搜索用时 15 毫秒
1.
曾六川 《数学物理学报(A辑)》2002,22(3):336-341
设犈是一致凸Banach空间,满足Opial条件或具有Frechet可微范数,犆是犈的非空闭凸子集,且犜:犆→犆是非扩张映象.又设对任何初始数据狓1 ∈犆,序列{狓狀}由下列修改了的Ishikawa迭代程序生成:狓狀+1 =狋狀犜狀(狊狀犜狀狓狀+ (1-狊狀)狓狀)+ (1-狋狀)狓狀, 狀≥1, (I)其中,数列{狋狀}与{狊狀}满足下列条件(i)和(ii)之一:(i)狋狀∈ [犪,犫]且狊狀∈ [0,犫];(ii)狋狀∈ [犪,1]且狊狀∈ [犪,犫],这里,常数犪,犫满足0<犪≤犫<1.作者证明了,犜有不动点的充要条件是,{狓狀}
弱收敛且{‖狓狀-犜狓狀‖}收敛到0.而且,由此即知,若犜有不动点,则{狓狀}弱收敛到犜的一个不动点. 相似文献
2.
Somyot Plubtieng Rattanaporn Punpaeng 《Journal of Mathematical Analysis and Applications》2007,336(1):455-469
In this paper, we introduce two iterative schemes by the general iterative method for finding a common element of the set of an equilibrium problem and the set of fixed points of a nonexpansive mapping in a Hilbert space. Then, we prove two strong convergence theorems for nonexpansive mappings to solve a unique solution of the variational inequality which is the optimality condition for the minimization problem. These results extended and improved the corresponding results of Marino and Xu [G. Marino, H.K. Xu, A general iterative method for nonexpansive mapping in Hilbert spaces, J. Math. Anal. Appl. 318 (2006) 43-52], S. Takahashi and W. Takahashi [S. Takahashi, W. Takahashi, Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaces, J. Math. Anal. Appl. 331 (1) (2007) 506-515], and many others. 相似文献
3.
本文研究弱一致Opial条件的性质;弱一致Opial条件与弱一致Opial条件的对偶性;证明当对偶空间有弱一致Opial条件时该Banach空间具有不动点性. 相似文献
4.
Brodskii and Milman proved that there is a point in C(K), the set of all Chebyshev centers of K, which is fixed by every surjective isometry from K into K whenever K is a nonempty weakly compact convex subset having normal structure in a Banach space. Motivated by this result, Lim et al. raised the following question namely “does there exist a point in C(K) which is fixed by every isometry from K into K?”. In fact, Lim et al. proved that “if K is a nonempty weakly compact convex subset of a uniformly convex Banach space, then the Chebyshev center of K is fixed by every isometry T from K into K”. In this paper, we prove that if K is a nonempty weakly compact convex set having normal structure in a strictly convex Banach space and F is a commuting family of isometry mappings on K then there exists a point in C(K) which is fixed by every mapping in F. 相似文献
5.
Jesús García-Falset Tomonari Suzuki 《Journal of Mathematical Analysis and Applications》2011,375(1):185-195
In this paper we introduce two new classes of generalized nonexpansive mapping and we study both the existence of fixed points and their asymptotic behavior. 相似文献
6.
该文研究局部凸空间中受集值约束的集值优化问题的超有效解. 证明了ic -锥-类凸集值映射的一个有用性质, 并以此性质为主要工具, 得到了ic -锥-类凸集值向量优化问题超有效解的最优性条件和鞍点定理. 相似文献
7.
An iterative algorithm is proposed for finding a fixed point of a nonexpansive self-mapping of a closed convex subset of a Banach space with a uniformly Gâteaux differentiable norm, and an estimate of the convergence speed also is given. 相似文献
8.
In this paper, we shall establish a fixed point property on Fréchet spaces for left reversible semitopological semigroups generalizing some classical results. 相似文献
9.
Nonexpansive mappings and asymptotic regularity 总被引:5,自引:0,他引:5
W. A. Kirk 《Nonlinear Analysis: Theory, Methods & Applications》2000,40(1-8):323-332
10.
In this paper, we introduce an iteration scheme given by finite nonexpansive mappings in Banach spaces and then prove weak convergence theorems which are connected with the problem of image recovery. Using the results, we consider the problem of finding a common fixed point of finite nonexpansive mappings. 相似文献