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.     

一类凹与凸算子的推广

运用锥的性质以及单调迭代技巧给出了一类广义凹算子与凸算子正不动点的存在唯一性,并讨论了算子特征值方程的性质.作为应用,利用所获结果研究了一类积分方程正解的存在唯一性.     

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.     

一类混合单调算子的不动点定理

运用锥理论与迭代方法,讨论了在较弱条件下一类混合单调算子的不动点的存在唯一性,所得结果是某些已有结果的本质改进和推广.     

EXISTENCE OF POSITIVE PERIODIC SOLUTIONS FOR INFINITE DELAY FUNCTIONAL DIFFERENTIAL EQUATIONS

In this paper, the existence of positive periodic solutions for infinite delay functional differential equations(FDEs for short) is discussed by utilizing a fixed point theorem on a cone in Banach space. Some results on the existence of positive periodic solutions are derived.     

利普希茨伪紧缩映射下的利普希茨摄动迭代的Bruck公式

在非线性分析中,处理伪紧缩算子及其变形的解(不动点)存在性和近似性,从而使演化方程的求解已经发展成为一个独立的理论.使用近似不动点技术,采用摄动迭代方法,目的是证明利普希茨伪紧缩映射序列的收敛性.该迭代方法适用于比利普希茨伪紧缩算子更一般的非线性算子以及Bruck迭代法无法证明其收敛性的情况.推广了Chidume和Zegeye的结果.