Banach空间中两个非扩张非自映象对公共不动点的逼近

设E是一致凸的Banach空间,C是E的非空有界闭凸子集而且是E的非扩张收缩核.设S,T:C→E是两个非扩张非自映象.本文证明了,在一定条件下,由(1.1)式定义的序列{xn}分别弱和强收敛于S,T的公共不动点.本文结果也推广和改进了最近一些人的最新结果.     

Existence and Uniqueness of Solutions for two Classes of Functional Equations Arising in Dynamic Programming

In this paper we establish the existence,uniqueness and iterative approximation of solutions fortwo classes of functional equations arising in dynamic programming of multistage decision processes.The resultspresented here extend,and unify the corresponding results due to Bellman,Bhakta and Choudhury,Bhaktaand Mitra,Liu and others.     

渐近非扩张映射变分不等式的不动点解

设X是实的Banach空间且有一致Gateaux可微范数和一致正规结构，C是X的非空闭凸子集，T，f分别是C上的渐近非扩张映射与压缩映射，X0∈C，xn＋1=anT^mXn＋（1-an）f（xn），n=0，1，2，…，当an∈（O，1）满足适当条件时，则{Xn）强收敛到某变分不等式的不动点解．     

Convergence theorems for a countable family of Lipschitzian mappings

This paper is concerned with convergence of an approximating common fixed point sequence of countable Lipschitzian mappings in a uniformly convex Banach space. We introduce a new condition for a class of mappings to obtain several weak and strong convergence theorems. This new condition is implied by many previous known conditions introduced by many authors. We also apply our results for a class of nonexpansive mappings and asymptotically nonexpansive mappings and we immediately obtain convergence theorems proved by Song-Chen, Kimura-Takahashi, Tan-Xu, and many others.     

Convergence theorem of common fixed points for Lipschitzian pseudocontraction semigroups in Banach spaces

The purpose of this paper is to study the convergence problems of the implicity iteration process for an asymptotically nonexpansive semigroups in general Banach spaces. The results presented in this paper extend and improve the corresponding results announced by many authors.     

Strong convergence of modified Ishikawa iteration for two asymptotically nonexpansive mappings and semigroups

In this paper, we established strong convergence theorems for a common fixed point of two asymptotically nonexpansive mappings and for a common fixed point of two asymptotically nonexpansive semigroups by using the hybrid method in a Hilbert space. Moreover, we also proved a strong convergence theorem for a common fixed point of two nonexpansive mappings. Our results extend and improve the recent ones announced by Kim and Xu [T.W. Kim, H.W. Xu, Strong convergence of modified Mann iteration for asymptotically nonexpansive mappings and semigroups, Nonlinear Anal. 64 (2006) 1140–1152], Nakajo and Takahashi [K. Nakajo, W. Takahashi, Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups, J. Math. Anal. Appl. 279 (2003) 372–379], and many others.     

非扩张映象对公共不动点的迭代逼近

对非扩张映象对引入了修改的Mann迭代格式，并证明了在一致光滑Banach空间中强收敛到其公共不动点，改进并推广了Tae—Hwa Kim and Hong—Kun Xu在2005年的结果．     

无限可数多个非扩展映像的公共不动点的迭代算法研究

Hilbert空间无限可数多个非扩展算子的公共点的不动点构造问题与可行性问题相关,Kikkawa和Takahashi证明了Hilbert空间中的一个强收敛定理.通过引入Mann迭代类型,得到新的迭代程序,改进了已有的混合迭代算法,使得迭代过程更具有可控性.     

Strong convergence theorems by hybrid methods for families of nonexpansive mappings in Hilbert spaces

In this paper, we prove a strong convergence theorem by the hybrid method for a family of nonexpansive mappings which generalizes Nakajo and Takahashi's theorems [K. Nakajo, W. Takahashi, Strong convergence theorems for nonexpansive mappings and nonexpansive semigroups, J. Math. Anal. Appl. 279 (2003) 372-379], simultaneously. Furthermore, we obtain another strong convergence theorem for the family of nonexpansive mappings by a hybrid method which is different from Nakajo and Takahashi. Using this theorem, we get some new results for a single nonexpansive mapping or a family of nonexpansive mappings in a Hilbert space.     

Implicit Iteration Scheme with Perturbed Mapping for Equilibrium Problems and Fixed Point Problems of Finitely Many Nonexpansive Mappings

We introduce an implicit iteration scheme with a perturbed mapping for finding a common element of the set of solutions of an equilibrium problem and the set of common fixed points of finitely many nonexpansive mappings in a Hilbert space. Then, we establish some convergence theorems for this implicit iteration scheme which are connected with results by Xu and Ori (Numer. Funct. Analysis Optim. 22:767–772, 2001), Zeng and Yao (Nonlinear Analysis, Theory, Methods Appl. 64:2507–2515, 2006) and Takahashi and Takahashi (J. Math. Analysis Appl. 331:506–515, 2007). In particular, necessary and sufficient conditions for strong convergence of this implicit iteration scheme are obtained. In this research, the first author was partially supported by the National Science Foundation China (10771141), Ph.D. Program Foundation of Ministry of Education of China (20070270004), and Science and Technology Commision of Shanghai Municipality Grant (075105118).