Banach空间中渐近非扩张映象具误差的强收敛定理

设E是一实的Banach空间,其范数是一致Gteaux可微的;D是E的一非空闭凸子集,设T:D→D是具有序列{k_n}[1,∞),lim_(n→∞) k_n=1的渐近非扩张映象.本文证明了,在一定条件下,由(1.3)和(1.5)式定义的具误差的迭代序列{x_n}强收敛于T的不动点.本文结果也推广和改进了最近一些人的最新结果.     

Sur un théorème de Castelnuovo

We continue the study of G. Castelnuovo on the group of birational transformations of the complex plane that fix each point of a curve of genus > 1 ; we use adjoint linear system of the curve as Castelnuovo does. We prove that these groups are abelian, and that these are either finite, of order 2 or 3, or conjuguate to a subgroup of the de Jonquières group. We show also that these results do not generalise to curves of genus ≤ 1. *Partiellement soutenu par le CNPq-Brasil et la Section de Mathématiques de l'Université de Genève.     

Existence of multiple fixed points for nonlinear operators and applications

In this paper, by the fixed point index theory, the number of fixed points for sublinear and asymptotically linear operators via two coupled parallel sub-super solutions is studied. Under suitable conditions, the existence of at least nine or seven distinct fixed points for sublinear and asymptotically linear operators is proved. Finally, the theoretical results are applied to a nonlinear system of Hammerstein integral equations.     

Common fixed point results for noncommuting mappings without continuity in cone metric spaces

The existence of coincidence points and common fixed points for mappings satisfying certain contractive conditions, without appealing to continuity, in a cone metric space is established. These results generalize several well-known comparable results in the literature.     

关于伪压缩映象不动点迭代的一点注记

设$K$是自反的并且具有一致Gateaux可微范数的Banach空间$E$的非空有界闭凸子集.设$T:K\rightarrow K$是一致连续的伪压缩映象.假设$K$的每一非空有界闭凸子集对非扩张映象具有不动点性质.设$\{\lambda_n\}$是$(0,\frac{1}{2}]$中序列满足: (i) $\lim_{n\rightarrow \infty}\lambda_n=0$; (ii) $\sum_{n=0}^{\infty}\lambda_n=\infty$.任给$x_1\in K$,定义迭代序列$\{x_n\}$为:$x_{n+1}=(1-\lambda_n)x_n+\lambda_nTx_n-\lambda_n(x_n-x_1),n\geq 1.$若$\lim_{n\rightarrow \infty}\|x_n-Tx_n\|=0$, 则上述迭代产生的$\{x_n\}$强收敛到$T$的不动点.     

渐近φ伪压缩映象有限族的迭代程序的强收敛(英文)

Strong convergence theorems for approximation of common fixed points of asymptoticallyφ-quasi-pseudocontractive mappings and asymptoticallyφ-strictly- pseudocontractive mappings are proved in real Banach spaces by using a new compos- ite implicit iteration scheme with errors.The results presented in this paper extend and improve the main results of Sun,Gu and Osilike published on J.Math.Anal. Appl.     

二阶共振周期边值问题多解的存在性

借助于与给定共振的非线性周期边值问题相关的非共振的线性边值问题来构造算子,利用范数形式的锥拉伸-压缩不动点定理,得到了非线性周期边值问题非负解的存在性定理.     

Iterative convergence theorems for maximal monotone operators and relatively nonexpansive mappings

In this paper, some iterative schemes for approximating the common element of the set of zero points of maximal monotone operators and the set of fixed points of relatively nonexpansive mappings in a real uniformly smooth and uniformly convex Banach space are proposed. Some strong convergence theorems are obtained, to extend the previous work.     

MULTIPLE POSITIVE SOLUTIONS TO SOME SECOND-ORDER m-POINT BOUNDARY VALUE PROBLEMS

Multiplicity of positive solutions to some second order m-point boundary value problems are considered. By fixed-point theorems in a cone, some new results are obtained. The associated Green’s function of these problems are also given.     

Systems of equilibrium problems with applications to new variants of Ekeland’s variational principle,fixed point theorems and parametric optimization problems

In this paper, we first establish some existence theorems of systems of generalized vector equilibrium problems. From these results, we obtain new variants of Ekeland’s variational principle in a Hausdorff t.v.s., a minimax theorem and minimization theorems. Some applications to the existence theorem of systems of semi-infinite problem, a variant of flower petal theorem and a generalization of Schauder’s fixed point theorem are also given.