无限族非扩张映象及非扩张半群的强收敛定理

目的是研究Banach空间中无限族非扩张映象和非扩张半群的强收敛问题.为此提出一个改进的迭代序列,在适当条件下,某些强收敛定理被证明.结果改进和推广了一些人的最新结果.     

On Rockafellar’s theorem using proximal point algorithm involving -maximal monotonicity framework

On the basis of the general framework of H-maximal monotonicity (also referred to as H-monotonicity in the literature), a generalization to Rockafellar’s theorem in the context of solving a general inclusion problem involving a set-valued maximal monotone operator using the proximal point algorithm in a Hilbert space setting is explored. As a matter of fact, this class of inclusion problems reduces to a class of variational inequalities as well as to a class of complementarity problems. This proximal point algorithm turns out to be of interest in the sense that it plays a significant role in certain computational methods of multipliers in nonlinear programming. The notion of H-maximal monotonicity generalizes the general theory of set-valued maximal monotone mappings to a new level. Furthermore, some results on general firm nonexpansiveness and resolvent mapping corresponding to H-monotonicity are also given.     

Resolvents of operators and partial functional differential equations with nonautonomous past

To a backward evolution family on a Banach space X we associate an abstract differential operator G through the integral equation on a Banach space of X-valued functions on . We compute the resolvent of the restriction of this operator to a smaller domain to obtain a generator. We then apply the results to prove existence, exponential stability and exponential dichotomy of solutions to partial functional equations with nonautonomous past as discussed in [S. Brendle, R. Nagel, Dist. Contin. Dynam. Systems 8 (2002) 953-966]. Our main tools are spectral mapping theorems for evolution semigroups and hyperbolicity criteria.     

序半群的阿基米德半群的半格分解

本文通过一个序半群S上的一些二元关系以及它的理想的根集的性质该序半群是阿基米德半群的半格,特别地是阿基米德半群的链的刻划,证明了S是阿基米德链当且仅当S是准素的.通过序半群的m-系的概念,证明了S的任意半素理想是含它的所有素理想的交,并通过该结论,证明了S是阿基米德半群的链当且仅当S是阿基米德半群的半格且S的所有素理想关于集包含关系构成链.作为应用,该结论在一般的半群（没有序）[1]中也成立.     

α-次积分半群的Trotter-kato定理

§１．　ＩｎｔｒｏｄｕｃｔｉｏｎＷｈｅｎｗｅｉｎｔｅｇｒａｔｅｄｉｆｆｅｒｅｎｔｉａｌｅｑｕａｔｉｏｎｓ，ｗｅｃａｎｆｏｒｍｕｌａｔｅｍａｎｙｏｆｔｈｅｍａｓａｎａｂｓｔｒａｃｔＣａｕｃｈｙｐｒｏｂｌｅｍ．ＡｎａｔｕｒａｌｑｕｅｓｔｉｏｎｉｎｔｈｅｔｈｅｏｒｙｉｓｔｏｆｉｎｄｓｕｉｔａｂｌｅｃｏｎｄｉｔｉｏｎｓｕｎｄｅｒｗｈｉｃｈａｓｅｑｕｅｎｃｅｏｆａａｂｓｔｒａｃｔＣａｕｃｈｙｐｒｏｂｌｅｍ．ｕ′ｎ＝Ａｎｕｎ（ｔ），ｕｎ（０）＝ｘｎ，ｆｏｒｔ≥０，ｎ＝１，２，…ｉｎａｎａｒｂｔｉｒａｒｙＢａ…     

Banach空间中一类映像的三重迭代法

利用赋范线性空间X的凸性模定义,以及凸性模的单调性及半紧性条件,研究了渐近非扩张映射不动点的三步迭代法.减弱了许多条件,从而推广了同类问题的某些结果.     

Smoothing properties of transition semigroups in hilbert spaces

The paper gives conditions under which the transition semigroup corresponding to a large class of semilinear equations on a Hilbert space transforms Borel functions onto Frechet differentia hies ones.     

On supercyclicity of operators from a supercyclic semigroup

We show that for every supercyclic strongly continuous operator semigroup {Tt}_t?0 acting on a complex F-space, every Tt with t>0 is supercyclic. Moreover, the set of supercyclic vectors of each Tt with t>0 is exactly the set of supercyclic vectors of the entire semigroup.     

ON THE ITERATIVE APPROXIMATION PROBLEM OF FIXED POINTS FOR ASYMPTOTICALLY NONEXPANSIVE TYPE MAPPINGS IN BANACH SPACES

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｒｏｕｇｈｏｕｔｔｈｉｓｐａｐｅｒｗｅａｓｓｕｍｅｔｈａｔＥｉｓａｒｅａｌＢａｎａｃｈｓｐａｃｅ ,Ｅ ｉｓｔｈｅｄｕａｌｓｐａｃｅｏｆＥ ,ＤｉｓａｎｏｎｅｍｐｔｙｓｕｂｓｅｔｏｆＥａｎｄＪ:Ｅ → 2 Ｅ ｉｓｔｈｅｎｏｒｍａｌｉｚｅｄｄｕａｌｉｔｙｍａｐｐｉｎｇｄｅｆｉｎｅｄｂｙＪ(ｘ) =ｆ∈Ｅ :〈ｘ ,ｆ〉 =‖ｘ‖·‖ｆ‖ ,　‖ｆ‖ =‖ｘ‖ (ｘ∈Ｅ) .　　Ｄｄｆｉｎｉｔｉｏｎ 1 1　ＬｅｔＴ :Ｄ →Ｄｂｅａｍａｐｐｉｎｇ1 )Ｔｉｓｓａｉｄｔｏｂｅａｓｙｍｐｔｏｔｉｃａｌｌｙｎｏ…     

FINITELY GENERATED COMMUTATIVE ARCHIMEDEAN SEMIGROUPS

In this work commutative Archimedean finitely generated semigroups are characterized in terms of ideal extensions.