局部凸空间的余逼近

研究了在局部凸空间中的ｆ－余逼近和强ｆ－余逼近的一些性质．     

局部凸空间中最佳逼近研究纵览

通过对大量文献研究，回顾了最佳逼近论的研究进展．重点讨论了最有意义的可分离局部凸空间最佳逼近问题、以及最佳逼近问题与向量优化、Pareto有效性、多值函数等之间的直接联系．     

局部凸空间中的不动点定理

证明了局部凸空间中非凸集上的上半连续凝集值映射的一个Ｌｅｒａｙ－Ｓｃｈａｕｄｅｒ型不动点定理,并推广了一些已知的不动点定理。     

局部凸拓扑向量空间中的不动点定理

本文在局部凸拓扑向量空间中得到了几个新的不动点定理，推广了［２］中的几个重要结果．     

局部凸可分离空间中的Drop定理

本文给出两个局部凸可分离空间中的Drop定理,其中一个严格强于丘京辉建立的结果,也严格强于郑喜印建立的结果(限制到局部凸可分离空间),另一个则使丘京辉提出的“局部凸空间中的弱序列紧凸子集具有弱Drop性质”这一定理的证明变得较为简单了．     

Lax定理在局部凸空间中的推广

本文给出Ｌａｘ定理在局部凸空间中的几个推广，特别地，我们获得Ｌａｘ定理的如下推广：设Ｘ和Ｙ为自反Ｆｒｅｃｈｅｔ空间，其拓扑分别由半范序列ｑ１≤ｑ２≤…和半范序列ｐ１≤Ｐ２≤…所给出．设Ａ：Ｙ→Ｘ′为连续线性算子，则存在连续线性算子Ｇ：Ｙ′→Ｘ使满足：（Ｇｇ，Ａｙ）＝（ｇ，ｙ），ｇ∈Ｙ′，Ｖ∈Ｙ当且仅当：对于ｎ，存在ｃｎ＞０，使ｓｕｐ｛１（Ａｙ，ｘ）｜：ｑｎ（ｘ）≤１｝≤ｃｎｐｍ．（ｙ），ｙ∈Ｙ且Ａ的值域在互Ｘ′中具拓扑补，这里，Ｘ′和Ｙ′分别记Ｘ和Ｙ的强对偶．     

局部凸空间的一致光滑性,一致凸性及有关逼近问题

研究了局部凸空间的某些几何性质，得到了局部凸空间为一致光滑的一个充分必要条件及局部凸空间为一致凸的若干等价条件，最后讨论了局部凸空间的有关逼近问题。     

局部凸空间的正规性

本文建立局部凸拓扑向量空间的正规性、完全正规性和单调正规性的等价条件．作为这些结果的应用，研究了函数空间的单调正规性和可度量性．     

Diestel-Faires定理在局部凸空间中的推广

通过Banach 空间与局部凸空间的对比,将Banach 空间上的Diestel-Faires 定理在局部凸空间上进行推广。进一步给出了局部凸空间上的Orlicz-Pettis定理与推论。     

Equicontinuous Seton Locally Convex Spaces

Ｌｅｔ（Ｅ，γ）ｂｅａｌｏｃａｌｌｙｃｏｎｖｅｘｓｐａｃｅａｎｄＥ′ｉｔｓｃｏｎｊｕｇａｔｅｓｐａｃｅ．ＡＥ′ｂｅａｎｅｑｕｉｃｏｎｔｉｎｕ－ｏｕｓｓｅｔｏｎ（Ｅ，γ）．ＴｈｅｗｅｌｌｋｎｏｗｎＡｌａｏｇｌｕ－ＢｏｕｒｂａｋｉＴｈｅｏｒｅｍ（［１］Ｐ２４８）ｓｔａｔｅｓｔｈａｔｅａｃｈｅ－ｑｕｉｃｏｎｔｉｎｕｏｕｓｓｅｔｏｎ（Ｅ，γ）ｉｓσ（Ｅ′，Ｅ）ｒｅｌａｔｉｖｅｌｙｃｏｍｐａｃｔｓｕｂｓｅｔ．Ｎｅｖｅｒｔｈｅｌｅｓｓ，ｅｑｕｉｃｏｎｔｉｎｕｏｕｓｓｅｔｉｓσ（Ｅ′，Ｅ）ｒｅｌａｔｉｖｅｌ…     

局部凸空间中的f-宽度

本文将赋范空间中的宽度推广到了局部凸空间,并得到了一些相应的结论.     

Locally Convex Spaces with Radon-Nikodym Property

Reflexive BANCH spaces and separable duals of BANACH spaces posses the RADON -NIKODYM Property. The purpose of this paper is to extend these results to locally convex spaces. As the examples will show, these RNP-spaces include most spaces which occur frequently in Functional Analysis.     

Maximization of Generalized Convex Functionals in Locally Convex Spaces

The major part of the investigation is related to the problem of maximizing an upper semicontinuous quasiconvex functional f over a compact (possibly nonconvex) subset K of a real Hausdorff locally convex space E. A theorem by Bereanu (Ref. 1) says that the condition f is quasiconvex (quasiconcave) on K is sufficient for the existence of maximum (minimum) point of f over K among the extreme points of K. But, as we prove by a counterexample, this is not true in general. On the further condition that the convex hull of the set of extreme points of K is closed, we show that it is sufficient to claim that f is induced-quasiconvex on K to achieve an equivalent conclusion. This new concept of quasiconvexity, which we define by requiring that each lower-level set of f can be represented as the intersection of K with some convex set, is suitable for functionals with a nonconvex domain. Under essentially the same conditions, we prove that an induced-quasiconvex functional f is directionally monotone in the sense that, for each y K, the functional f is increasing along a line segment starting at y and running to some extreme point of K. In order to guarantee the existence of maximum points on the relative boundary r K of K, it suffices to make weaker demands on the function f and the space E. By introducing a weaker kind of directional monotonicity, we are able to obtain the following result: If f is i.s.d.-increasing i.e., for each y y K, there is a half-line emanating from y such that f is increasing along this half-line, then f attains its maximum at rK , even if E is a topological linear Hausdorff space (infinite-dimensional and not necessarily locally convex). We state further a practical method of proving i.s.d.-monotonicity for functions in finite-dimensional spaces and we discuss also some aspects of classification.     

Linear Monotone Subspaces of Locally Convex Spaces

The main focus of this paper is to study multi-valued linear monotone operators in the context of locally convex spaces via the use of their Fitzpatrick and Penot functions. Notions such as maximal monotonicity, uniqueness, negative-infimum, and (dual-)representability are studied and criteria are provided.     

Proper Efficiency in Locally Convex Topological Vector Spaces

We present a general treatment of proper efficiency, which was originally given in normed vector spaces; we introduce a new kind of efficiency in locally convex topological vector spaces. We examine the relationships among these efficiencies. As an application, we prove a strong Ekeland variational principle.     

Weakly Unconditional Cauchy Series on Locally Convex Spaces

Ｗｅａｋｌｙ　Ｕｎｃｏｎｄｉｔｉｏｎａｌ　Ｃａｕｃｈｙ　Ｓｅｒｉｅｓ　ｏｎ　Ｌｏｃａｌｌｙ　Ｃｏｎｖｅｘ　ＳｐａｃｅｓＬｉＲｏｎｇｌｕ（李容录）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＨａｒｂｉｎＩｎｓｔｉｔｕｔｅｏｆＴｅｃｈｎｏｌｏｇｙ，...