关于多值映象连续性的两个例子

本文在R²中构造了两个十分简单的多值映象的例子:第一个说明准上半连续(?)上半连续;第二个说明弱上半连续(?)准上半连续。     

有界闭凸值测度的集值积分

引入实值函数关于有界闭凸值测度的集值积分,并讨论了集值积分的收敛定理,证明了当集值测度为有界闭凸集值的有界变差集值测度时,关于弱紧凸集值测度的积分性质对有界闭凸集值测度仍然保持.推广了实值函数关于弱紧凸值测度的积分.     

有限区间上的函数K〈1集压缩映象的性质

有界闭集上的函数K<1集压缩映象是紧压缩映象，且是闭映象，有界闭凸集到自身的函数K<1集压缩映象一定有不动点。     

有限区间上的函数K<1集压缩映象的性质

有界闭集上的函数Ｋ＜１集压缩映象是紧压缩映象，且是闭映象．有界闭凸集到自身的函数Ｋ＜１集压缩映象一定有不动点．     

对没有凸值和连续性的集值映象的最佳逼近定理*

本文引入和研究了一类具有弱凸图的集值映象.对这类映象证明了某些新的重合定理,最佳逼近和不动点定理.     

积分凸性及其应用

该文在Banach空间中通过向量值函数的Bochner积分引进集合与泛函的积分凸性以及集合的积分端点等概念. 文章主要证明有限维凸集、开凸集和闭凸集均是积分凸集，下半连续凸泛函与开凸集上的上半连续凸泛函均是积分凸的, 非空紧集具有积分端点, 对紧凸集来说其积分端点集与端点集一致, 最后给出积分凸性在最优化理论方面的两个应用.     

对没有凸值的连续性的集值映象的最佳逼近定理

本和引入和研究一类具有弱凸图的集值映象，对这类映象证明了某些新的重合定理，最佳逼近和不动点定理。     

Hilbert空间中的非扩张映象的不动点集的结构及其迭代集合序列逼近

我们研究Hilbert空间H中的闭凸集C上的非扩张映象T的不动点集F(T)的结构和它的集合序列逼近。我们得到 1 不动点集F(T)是闭的和凸的; 2 提供一个集合序列迭代法,使得由这个方法构造的迭代集合序列在某些条件和某种意义下强(弱)收敛于T的一个不动点,并给出收敛速度估计。 前面叙述的这些结果包含了Browder,Petryshyn,Kirk等人的某些结果。     

超凸空间中的选择定理及弱外超凸集的性质

本文利用半序方法,研究具有外超凸集值的带次可加模的集值映象的保不动点集,带相同次可加模的单值选择,获得了这类单值选择的存在性及唯一性条件.且研究了弱外超凸集的一些相交性质.     

非紧域上集值映象的重合点与不动点

在赋范线性空间的非空非紧凸集上建立了集值映象对的一个重合点定理,然后用这一定理改进了文献［１］中的集值映象内向集定理与外向集定理,并得到几个集值映象不动点定理．     

Cn中拟凸映射和星形映射的系数问题

§ 1.　Introduction　　Theconvexfunctionshavebeenextensivelystudiedinonecomplexvariable .Thesefunc tionsareeasilycharacterizedbysimpleanalyticorgeometricconditionsandtherearemanywellknownresultswhichcanhelpusunderstandtheirnature.However,thedifficultiesariseinsev eralcomplexvariables.Imposingtheconditionthatamappingbeconvexmappingturnsouttobeveryrestrictiveandsothefamilyofquasi convexmappingswasintroducedbyROPERKAandSUFFRIDGETJin [1 ].In [2 ]wehaveshown :thefamilyofquasi convexmappings…     

A Note on Burkholder Integrals

In this note, for $k$-quasiconformal mappings of a bounded domain into the complex plane, we give an upper bound of Burkholder integral. Moreover, as an application we obtain an upper bound of the $L^p$-integral of $\sqrt{J_f}$ and $|Df|$ for certain $K$-quasiconformal mappings.     

Lower Semicontinuous Regularization for Vector-Valued Mappings

The paper is devoted to studying the lower semicontinuity of vector-valued mappings. The main object under consideration is the lower limit. We first introduce a new definition of an adequate concept of lower and upper level sets and establish some of their topological and geometrical properties. A characterization of semicontinuity for vector-valued mappings is thereafter presented. Then, we define a concept of vector lower limit, proving its lower semicontinuity, and furnishing in this way a concept of lower semicontinuous regularization for mappings taking their values in a complete lattice. The results obtained in the present work subsume the standard ones when the target space is finite dimensional. In particular, we recapture the scalar case with a new flexible proof. In addition, extensions of usual operations of lower and upper limits for vector-valued mappings are explored. The main result is finally applied to obtain a continuous D.C. decomposition of continuous D.C. mappings. Dedicated to Alex Rubinov in honor of his 65th birthday     

Modified continuity and a generalisation of Michael's selection theorem

We modify the definitions of continuity and lower semicontinuity for single-valued mappings and upper and lower semicontinuity for set-valued mappings. For single-valued mappings we have a generalisation of Osgood's theorem and for set-valued mappings we have an extension of Fort's theorem and a generalisation of Michael's selection theorem producing a densely defined selection with a natural continuity property relative to the domain.     

α次殆β型螺形映照齐次展开式的精细估计

从Loewner链的角度讨论C~n中单位球B~n上α次殆β型螺形映照齐次展开式的相关项的上界,并作为特殊情况得出β型螺形映照、星形映照和α次殆星形映照齐次展开式的相关项的上界估计,推广了螺形映照及星形映照齐次展开式的二次项系数的上界估计.     

Integral means and arclength inequalities for typically real logharmonic mappings

In this paper, we use star functions to conclude the integral means inequalities for typically real logharmonic mappings. Moreover, we determine the upper bound for the arclength of typically real logharmonic mappings.     

Data volume reduction in covering approximation spaces with respect to twenty-two types of covering based rough sets

In this paper, we investigate whether consistent mappings can be used as homomorphism mappings between a covering based approximation space and its image with respect to twenty-two pairs of covering upper and lower approximation operators. We also consider the problem of constructing such mappings and minimizing them. In addition, we investigate the problem of reducing the data volume using consistent mappings as well as the maximum amount of their compressibility. We also apply our algorithms against several datasets.     

The Generic Stability of Fixed Points for Upper Semicontinuous Mappings in Hyperconvex Metric Spaces

The main goal of this paper is to establish the generic stability of Fan-Glicksberg type fixed points in hyperconvex metric spaces. In order to do so, we first give Fan-Glicksberg type fixed point theorem in hyperconvex metric spaces and then the generic stability of fixed points for upper semicontinuous set-valued mappings is obtained. Our generic stability results show that almost all of fixed points of upper semicontinuous set-valued mappings defined in compact hyperconvex metric spaces are stable in the sense of Baire category theory     

Distortion theorems for subclasses of starlike mappings along a unit direction in ℂ

In this paper, we obtain a distortion theorem of Jacobian matrix for biholomorphic subclasses of starlike mappings along a unit direction on the unit polydisc. These results extend the classical distortion theorem of starlike mappings to higher dimensions. We then give an upper bound estimate for biholomorphic subclasses of starlike mappings along a unit direction in a complex Banach space.     

Kuratowski convergence of the efficient sets in the parametric linear vector semi-infinite optimization

In the space of whole linear vector semi-infinite optimization problems we consider the mappings putting into correspondence to each problem the set of efficient and weakly efficient points, respectively. We endow the image space with Kuratowski convergence and by means of the lower and upper semi-continuity of these mappings we prove generic well-posedness of the vector optimization problems. The connection between the continuity and some properties of the efficient sets is also discussed.