双连续n次积分C余弦函数的逼近定理

基于双连续半群概念,引入一致双连续半群序列概念,借助Laplace变换和Trotter-Kato定理,考察双连续n次积分C余弦函数与C-预解式之间的关系,得到逼近定理的稳定性条件,进而得出双连续n次积分C余弦函数逼近定理.从而对Banach空间强连续半群逼近定理和双连续半群逼近定理进行了推广,为相应抽象的Cauchy问题提供了解决方案.     

弱对称Markov积分半群的表示

本文研究了弱对称Markov积分半群的表示.利用积分的方法,获得了弱对称Markov积分半群的Kendall和Karlin-McGregor表示,推广了转移函数的Kendall和Karlin-McGregor表示.     

随机单调Markov积分半群

讨论了Markov积分半群的单调性和转移函数的单调性的等价性,并得到最小的Q半群是单调的充要条件.     

Markov积分算子半群的限制及关于增加积分算子半群的生成

证明了转移函数是l∞的一个子空C^1上的正的压缩C0半群，其极小生成元恰好是Markov积分算子半群的生成元在C^1中的部分；Markov积分算子半群的生成元稠定的充分必要条件是q-矩阵Q一致有界；同时转移函数是Feller—Reuter—Riley的充要条件是Markov积分算子半群的生成元在Cn中的部分产生一个强连续半群．最后，在序Banach空间给出了增加的压缩积分算子半群的生成定理．     

关于n次积分C半群的扰动

研究了n次积分C半群的可交换扰动问题,得到其扰动定理;并根据n次积分C半群与C半群的关系得到了n次积分C半群的两个乘积扰动定理.     

双连续N次积分C-半群的逼近定理

在C0半群和双连续半群逼近定理的启发下,讨论了双连续n次积分C-半群的逼近定理.     

α次积分半群的扰动

在n次积分半群及一次积分半群扰动理论的基础上,探讨了α次积分半群的扰动性,得到了α次积分半群的扰动定理.     

a次积分C-半群的扰动

在α次积分半群的扰动理论的基础上,讨论了α次积分C-半群的可交换扰动问题,得到了α次积分D半群的扰动定理.     

指数有界双连续α次积分C半群的扰动

在α次积分C半群和双连续n次积分C半群的基础上,探讨了双连续α次积分C半群的扰动性,得到了双连续α次积分C半群的扰动定理,并且在局部Lipschitz连续条件下证明双连续α次积分C半群的扰动理论仍然成立.     

指数有界的C余弦算子函数

本文引入了指数有界的Ｃ余弦算子函数的生成元，讨论了生成元的基本性质，建立了相应的生成定理、逼近定理及扰动定理．最后给出了指数有界的Ｃ余弦算子函数与指数有界的Ｃ半群的基本联系．     

The Study of KKM Theorems With Applications to Vector Equilibrium Problems and Implict Vector Variational Inequalities Problems

In this paper, we establish some equivalence relations between coincidence theorems and KKM-type theorems. We also obtain some new coincidence theorems and fixed point theorems. Applying the KKM-type theorems we obtain the existence theorems of generalized vector equilibrium problems. From these results, some existence theorems of generalized vector implicit variational inequality problems are established in this paper.     

Operator Ergodic Theorems for Actions of Free Semigroups and Groups

New ergodic theorems are obtained for measure-preserving actions of free semigroups and groups. These theorems are derived from ergodic theorems for Markov operators. This approach also allows one to obtain ergodic theorems for some classes of Markov semigroups. Results of the paper generalize classical ergodic theorems of Kakutani, Oseledets, and Guivarc'h, and recent ergodic theorems of Grigorchuk, Nevo, and Nevo and Stein.     

Applications of Michael's selection theorems to fixed point theory

Applying some of Ernest Michael's selection theorems, from recent fixed point theorems on u.s.c. multimaps, we deduce generalizations of the classical Bolzano theorem, several fixed point theorems on multimaps defined on almost convex sets, almost fixed point theorems, coincidence theorems, and collectively fixed point theorems. These results are related mainly to Michael maps, that is, l.s.c. multimaps having nonempty closed convex values.     

超凸空间中的连续选择定理与耦合定理

本文给出了超凸空间中的连续选择定理与耦合定理，并得到了它们的证明,作为应用，我们给出了超凸空间中的不动点定理与截口定理．     

Fixed point theorems for better admissible multimaps on almost convex sets

We obtain new fixed point theorems on multimaps in the class Bp defined on almost convex subsets of topological vector spaces. Our main results are applied to deduce various fixed point theorems, coincidence theorems, almost fixed point theorems, intersection theorems, and minimax theorems. Consequently, our new results generalize well-known works of Kakutani, Fan, Browder, Himmelberg, Lassonde, and others.     

多元Stancu算子的Boolean和迭代

定义单纯形上高维Stancu算子的Boolean和迭代算子并且研究它逼近连续函数的正定理、逆定理与饱和定理，得到了较高的逼近阶．     

奇数维spin~c流形和S~1作用(英文)

本文研究了奇数维spin~c流形上的等边指标定理.用这些指标定理和一些复分析的讨论,得到了两个奇数维spin~c流形上的Atiyah-Hirzebruch类型消灭定理,结果推广了刘-王的消灭定理.     

Generalized KKM theorems on hyperconvex metric spaces and some applications

In this work, we establish the intersection property for a family of admissible subsets in a hyperconvex metric space, and we apply this intersection property to get generalized KKM theorems, coincidence theorems, variational inequality theorems and minimax inequality theorems.     

G-凸度量空间中的广义KKM定理及其应用

在一类新的G-凸度量空间中建立了一类新的KKM定理,统一、改进和发展了文献中的相应结果.作为应用,得到了几个新的匹配定理和不动点定理.     

Φ-Conjugation and noneonvex optimization. a survey (part III)

In the present paper, which is part III of our review concerning the theory of Φ-conjugate functions, we consider Lagrangians, duality theorems are proved and the connection to saddle point theorems is shown. By a fundamental inequality, duality theorems are proved and the connection to saddle point theorems is shown. By a fundamental inequality, duality theorems can be obtained, where results are modified given in part I and part II of our paper.