一致凸的

Based on the concepts of asymptotic center point and the asymptotic radius, this paper discusses the existence and the weak convergence of the fixed point in the multi_valued asymptotically nonexpansive mappings.

本文借助于渐近中点、渐近半径的概念，得到一致凸Banach空间中非空有界闭凸子集上的连续集值渐近非扩张映射有不动点。

However, if the polygon is convex, then the bimedial and bisector skeletons will coincide and each subpolygon will be convex.

但是，如果原外围多边形本身是凸的，则中间线骨架与角分线骨架一致，且每个子多边形也均为凸。

Let X be a reflexive Banach space with both X and X locally uniformly convex. D is a bounded, open, convex subset of X. T∶D→X is a pseudo-monotone operator; C∶D→X is a compact or strongly continuous operator.

何震设X是自反Banach空间且X和X均为局部一致凸空间，D是X的开、有界、凸子集， T∶D→X是伪单调算子(pseudo-monotone)， C∶D→X是紧算子或全连续算子。

Tan and Xu [1] had proved the theorem on convergence of Ishikawa iteration processes of asymptotically nonexpansive mapping on a compact convex subset of a uniform convex Banach space , Then Liu Qihou [3] presents the necessary and sufficient conditions for the Ishikawa iteration of asymptotically quasi-nonexpansive mapping with an error member on a Banach space convergent to a fixed point . Xu and Noor [5] had proved the theorem on convergence of three-step iterations of asymptotically nonexpansive mapping on nonempty closed, bounded and convex subset of uniformly convex Banach space.

Tan和Xu已经证明了建立在一致凸Banach空间紧凸子集上的渐进非扩张映射的Ishikawa迭代序列的收敛原理，随之，刘齐侯又阐述了Banach空间上渐进准非扩张映射T的具误差的Ishikawa迭代序列收敛于T的不动点的充分必要条件；之后，Xu和Noor也证明了定义在一致凸Banach空间某非空有界闭凸子集上的渐进非扩张映射的三步迭代序列的收敛原理。

Ruck, Hirano and Reich extended Baillon抯 theorem to a uniformly convex Banach space with a Frechet differentiable norm. Hirano-Kido-Takahashi, Oka, Park and Jenong proved the ergodic theorem for commutative semigroups of nonexpansive mappings and asymptotically nonexpansive mappings in the uniformly convex I3anach space with the Frechet differentiable nonn.

aillon的定理被Bruck，Hirano及Reich推广到具Frechet可微范数的一致凸Banach空间中，而当G是一般交换拓扑半群时，Hirano-Kido-Takahashi，Oka，Park及Jeong分别给出了具Frechet可微范数的一致凸Banach空间中非扩张半群及渐近非扩张半群的遍历压缩定理和遍历收敛定理。

Furthermor, we consider their nondiferentiable situation, we define nonsmooth univex functions for Lipschitz functions by using Clarke generalized directional derivative and study nonsmooth multiobjective fractional programming with the new convexity. We establish generalized Karush-Kuhn-Tucker necessary and sufficient optimality condition and prove weak, strong and strict converse duality theorems for nonsmooth multiobjective fractional programming problems containing univex functions.

而且，本文利用Clarke广义方向导数针对Lipschitz函数在原来一致凸函数概念的基础上定义了不可微的一致凸函数，并利用这类新凸性，我们研究了非光滑多目标分式规划，获得了广义Karush-Kuhn-Tucher最优性条件；弱对偶定理、强对偶定理和严格逆对偶定理。

In chapter 4 , with S-KKM mapping , a new Ky Fan\'s minimax inequality is proved , the locally convex H-space with uniform structure is introduced , s-HKKM mapping is defined as the generalization of KKM mapping, with the H-convexity of Hausdorff locally convex H-space , a new fixed point theorem for the compact andclosed mapping belonging to the class s-HKKM is established ;with local intersection property of muti-function ,K-H-quasi-convexity of mapping , connectedness of set and condensing correspondences, some new vector quasi-variational inequalities are established , respectively .

第四章利用S-KKM映射，建立了新的Ky Fan极小极大不等式；定义了带有一致结构的局部凸H-空间，利用Hausdorff局部凸H-空间的H-凸性，对于属于s-HKKM中紧的闭映射建立了新的不动点定理，利用对应的局部交性质、映射的K-拟-凸性、集合的连通性以及φ-condensing对应分别建立了相应的拟向量变分不等式。

In chapter 5, we investigate uniformly starlike and uniformly convex mappings on the unit ball in C〓, give a criterion for the latter, and obtain some results which are similar to Harnack inequalities. Hence the contents of these two mappings are richened a little.

第五章主要研究多复变数的一致星形映射和一致凸映射，给出一致凸映射的一个判别准则，并且得到关于这两个映射的类似于Harnack不等式的结果，从而使得有关这两类映射的研究内容更加丰富。

For example, U-space is uniformly regular and which makes it has fixed point property, U-space is uniformly non-square and thus super-reflexive, uniformly convex space and uniformly smooth space are U-spaces, and an Banach space is an U-space iff its dual space is U-space, etc. In1990s, a lot of work had been done on U-space theory, e.g., Tingfu Wang and Donghai Ji introduced the concepts of pre U-property and nearly U-property. Under the structure of Orlicz space, they made systematic investigation of these properties, and gave the criteria for an Orlicz space to have U-property.

U-空间具有一致正规结构进而具有不动点性质；U-空间是一致非方的，进而也是超自反的；一致凸空间和一致光滑空间是U-空间；Banach 空间为U-空间的充要条件是其对偶空间为U-空间，等等。20世纪90年代，国内外学者对U-空间理论做了很多工作，王廷辅，计东海等人先后引入了准U-性质与似U-性质的概念，并在Orlicz空间框架下对有关性质进行了系统研究，完整给出了Orlicz空间具有各种U-性质的判据。

Clarkson introduced the concept of convex modulus while researching uniformly convex spaces, later the relations between numbers of convex modulus and relevant geometric properties had been drawn.

同年，J.Clarkson在研究一致凸时引入了凸性模的定义，而后，人们从多侧面得出了凸性模的取值与相关几何性质之间的关系。

This one mode pays close attention to network credence foundation of the businessman very much.

这一模式非常关注商人的网络信用基础。

Cell morphology of bacterial ghost of Pasteurella multocida was observed by scanning electron microscopy and inactivation ratio was estimated by CFU analysi.

扫描电镜观察多杀性巴氏杆菌细菌幽灵和菌落形成单位评价遗传灭活率。