增算子的不动点和广义不动点

本文在紧性条件下证明了若干新的非连续的增算子的不动点定理.如果不假定增算子 A 满足连续性条件和紧性条件,我们证明了算子 A 有广义不动点.     

序Banach空间中不连续增算子的不动点

本文在较弱的紧性条件下,给出了序Banach空间中不连续增算子的不动点的存在性结果．     

有序Banach空间中的拟弱收敛及其应用

在有序Ｂａｎａｃｈ 空间中引入拟弱收敛,并表明拟弱收敛弱于弱收敛·　由此,在非紧性条件下,获得了非连续增算子的不动点,并将它应用于Ｈａｍｍｅｒｓｔｅｉｎ 型非线性积分方程     

非连续弱紧增算子的不动点及其对Banach空间初值问题的应用

证明了Banach空间上一类非连续的弱紧增算子的不动点定理,特别获得了最大不动点与最小不动点的存在性,改进了已有的某些结果.作为应用,讨论了Banach空间中含间断项的常微分方程初值问题最大解与最小解的存在性.     

半序线性空间中混合单调映射不动点的存在唯一性

本文研究半序线性空间中一类混合单调映射不动点的存在唯一性及其迭代方法,对所述映射没作连续性或紧性假定．其推论改进了序Banach空间中增算子与减算子的某些已知结果．最后把所得结论用于常微分方程奇异边值问题．     

FC-空间中的不动点定理及其对广义拟平衡问题系统的应用

建立了非紧FC-空间中弱转移紧开值映射的不动点定理,作为应用,获得非紧FC-空间中广义拟平衡问题系统的平衡存在定理.     

具集值映射的广义强向量拟均衡问题

讨论了一类具集值映射的广义强向量拟均衡问题（GSVQEP）解的存在性.利用连续选择定理和不动点定理,在没有任何单调性假设下得到了GSVQEP解的存在性定理.     

一类增算子的不动点定理的推广及应用

利用锥理论单调迭代技巧,研究Banach空间中不具有任何紧性、连续性和凹凸性条件的增算子的不动点的存在唯一性,所得结果改进和推广了增算子的某些已知相应结果.     

一致等度连续的渐近拟伪压缩型映象的强收敛性

设E是实赋范线性空间.K是E中的非空凸子集.T1,T2是K上的自映象.当T1是一致等度连续的渐近拟伪压缩型映象,T2是广义一致Lipschitz映象时,研究了具误差的Isikawa型迭代序列强收敛于T1,T2公共不动点的充要条件.所得结果推广和改进了近期内的相应结果.     

Banach空间中渐近拟非扩张映象的具误差Ishikawa迭代序列(英文)

本文我们证明了Banach空间中渐近拟非扩张映象T的具误差Ishikawa迭代过程收敛到不动点的一个充要条件 ,其中T不要求连续 .我们的定理推广了近期的相应结果 .     

偏好意义下的Pareto极值存在性定理及其应用

本文给出了偏好意义下的Ｐａｒｅｔｏ极值存在性定理．作为应用,得到了推广的Ｗｅｉｅｒｓｔｒａｓｓ定理以及非连续集值增算子的不动点定理．     

On ℒ Characteristic of Some Potential Type Operators with Oscillating Symbols and Singularities of the Kernels on a Sphere

We obtain some new existence theorems for the maximal and minimal fixed points of discontinuous increasing operators. As applications, we consider the existence of the maximal and minimal solutions of nonlinear integro-differential equations with discontinuous terms in Banach spaces. Our results generalize and improve many well-known conclusions. This revised version was published online in June 2006 with corrections to the Cover Date.     

Fixed points for mixed monotone multivalued operators in Banach spaces with applications

In this paper, the existence and iterative approximation of fixed points for a class of systems of mixed monotone multivalued operator are discussed. We present some new fixed point theorems of mixed monotone operators and increasing operators which need not be continuous or satisfy a compactness condition. We also give some applications to differential inclusions with discontinuous right hand side in Banach spaces and to Hammerstein integral inclusions on RN.     

Banach空间中含间断项的二阶非线性常微分方程周期边值问题

在Banach空间中利用上下解方法与不连续增算子不动点定理，研究了含间断项和右端函数具有一阶导数项的二阶非线性常微分方程周期边值问题的最大解、最小解的存在性，推广和改进了现有的结果．而且对于有限维空间，我们获得的这些结果也都是新的．     

Fixed points of discontinuous multivalued increasing operators in Banach spaces with applications

By using relatively weakly compactness conditions, we obtain existence theorems of fixed points for discontinuous multivalued increasing operators in Banach spaces. As an application, we utilize the results obtained in Section 2 to lead to the existence principles for integral inclusions of Hammerstein type multivalued maps.     

Fixed points of generalized e-concave (generalized e-convex) operators and their applications

In this paper, we present the definitions of generalized e-concave operators and generalized e-convex operators, which are the generalizations of e-concave operators and e-convex operators, respectively. Without compactness or continuity assumption of generalized e-concave operators and generalized e-convex operators, we have proved the existence, uniqueness and monotone iterative techniques of their fixed points. Our results are even new to e-concave operators and e-convex operators. Finally, we apply the results to the singular boundary value problems for second order differential equations.     

一类混合单调算子的耦合不动点定理及其应用

讨论了一类混合单调算子的耦合不动点定理,并获得了最大最小耦合不动点.作为应用,讨论了Banach空间中含有不连续项的混合单调Volterra型积分方程耦合拟解的存在性问题.     

Error Estimate of Data Dependence for Discontinuous Operators by New Iteration Process with Convergence Analysis

Abstract

In this paper, we introduce a new discontinuous operator and investigate the existence and uniqueness of fixed points for the operators in complete metric spaces. We also provide rate of convergence and data dependency of S-iterative scheme for a fixed point of the discontinuous operators in Banach spaces. Moreover, we prove the estimation Collage theorems and compare error estimate between data dependency and Collage theorems. Numerical examples are provided to support our results.     

On elliptic systems with discontinuous nonlinearities

In this paper we deal with elliptic systems with discontinuous nonlinearities. The discontinuous nonlinearities are assumed to satisfy quasimonotone conditions. We shall use the method of upper and lower solutions with fixed point theorems on increasing operators in ordered Banach spaces to show some existence theorems.