FC-空间上的鞍点定理及应用

在不具有任何凸性结构和线性结构的有限连续空间(简称FC-空间)中给出了一个鞍点定理.并应用此定理,在很弱的条件下证明了一些非空交定理及截口定理,推广了近期文献中的一些相关的结果.     

FC-空间上的选择定理与应用

在FC-空间中给出了选择定理,证明了一些非空交定理,推广了近期文献中的一些相关的结果.     

G-凸空间中的KKM定理，匹配定理和截口定理

在G-凸空间中证明了一些新的KKM型定理．作为应用,在G-凸空间中得到了一些新的匹配定理和截口定理,所得结果改进和推广了[2,3,7]中的相关结果．     

相关Yetter-Drinfel'd Hopf代数上的相关Hopf模结构定理

主要证明了相关Yetter-Drinfel'd Hopf代数上的相关Hopf模结构定理,不仅推广了Yetter-Drinfel'd Hopf代数上的Hopf模结构定理,而且推广了相关Hopf模结构定理.同时,给出相关Yetter-Drinfel'd Hopf代数上的Maschke定理.     

拓扑空间中的一个非空交定理及其应用

在FC-空间中证明了一新的非空交定理．作为应用，一不动点定理，一极大元定理，一重合点定理和一些极小极大不等式被证明．这些定理推广了近期文献中的结果．     

Caristi 不动点定理的推广及应用

本文推广了古典的Garisti不动点定理,作为应用,古典的Ekeland变分原理得到了推广,并且证明了推广的Garisti不动点定理和推广的Ekeland变分原理是等价的．     

Banach空间中多值映象的不动点定理

本文中我们首先证明了一个不动点定理，同时从压缩及弱内向两个方向推广了压缩弱内向映象的不动点定理［１，２］．在后两节中讨论了Ｂａｎａｃｈ空间中无界闭子集上的不动点定理，所得结果推广了［３，４］中相应定理．     

G-凸空间内新的聚合不动点定理及应用

由应用连续单位分解技巧和Tychonoff不动点定理对定义在非紧G－凸空间的乘积空间上的一族集值映象证明了一些新的不动点定理。作为应用，对G－凸空间的乘积空间的一簇子集证明了Ky Fan型非空交定理；在G－凸空间内给出了非线性不等式组解的一个存在定理和得到了一些抽象经济的平衡存在定理，这些定理改进和推广了很多最近文献中重要的已知结果。     

积分中值定理的逆问题

研究积分第一中值定理,提出推广的积分第一中值定理逆问题的一个定理,为证明该定理,给出了两个引理,并通过构造辅助函数及集合,运用介值定理证明了两个引理,最后应用两个引理证明了该定理。     

零调复合映象的重合定理和最佳逼近定理

对定义在可缩空间上的零调值复合映象证明了某些新的重合点定理.作为应用某些最佳逼近定理和集值映象的重合点定理被给出.这些定理改进和推广了最近文献中许多已知结果.     

A generalization of the Gauss-Lucas theorem

Given a set of points in the complex plane, an incomplete polynomial is defined as the one which has these points as zeros except one of them. The classical result known as Gauss-Lucas theorem on the location of zeros of polynomials and their derivatives is extended to convex linear combinations of incomplete polynomials. An integral representation of convex linear combinations of incomplete polynomials is also given.     

Fenchel's duality theorem in generalized geometric programming

Fenchel's duality theorem is extended to generalized geometric programming with explicit constraints—an extension that also generalizes and strengthens Slater's version of the Kuhn-Tucker theorem.This research was sponsored by the Air Force Office of Scientific Research, Air Force Systems Command, USAF, under Grant No. AFOSR-73-2516.     

A drop theorem without vector topology

Daneš' drop theorem is extended to bornological vector spaces. An immediate application is to establish Ekeland-type variational principle and its equivalence, Caristi fixed point theorem, in bornological vector spaces. Meanwhile, since every locally convex space becomes a convex bornological vector space when equipped with the canonical von Neumann bornology, Qiu's generalization of Daneš' work to locally convex spaces is recovered.     

A probabilistic approach to the maximal diameter theorem

Under a positive curvature and a finite dimension in terms of the Bakry‐Émery tensor on a Riemannian manifold, the Bonnet‐Myers type diameter bound and the rigidity theorem are extended. The corresponding second order generator need not be symmetrizable. The proof is based on the Laplacian comparison theorem and stochastic analysis of radial processes.     

The local inverse mapping theorem on Banach orbifolds

In this note, the local inverse mapping theorem is extended to a class of Banach orbifolds.     

A strong limit theorem on gambling systems

A strong limit theorem on gambling system for Bernoulli sequences is extended to the sequences of arbitrary discrete random variables by using the conditional probabilities. Furthermore, by allowing the selection function to take values in an interval, the conception of random selection is generalized. In the proof an approach of applying the differentiation of measure on a net to the investigation of the strong limit theorem is proposed.     

Full analogy of Sharkovsky's theorem for lower semicontinuous maps

A full analogy of the celebrated Sharkovsky cycle coexistence theorem is established for lower semicontinuous (multivalued) maps on metrizable linear continua. This result is further extended to triangular maps.     

Local completeness, drop theorem and Ekeland's variational principle

By using a very general drop theorem in locally convex spaces we obtain some extended versions of Ekeland's variational principle, which only need assume local completeness of some related sets and improve Hamel's recent results. From this, we derive some new versions of Caristi's fixed points theorems. In the framework of locally convex spaces, we prove that Daneš' drop theorem, Ekeland's variational principle, Caristi's fixed points theorem and Phelps lemma are equivalent to each other.     

Fueter's theorem: The saga continues

In this paper is extended the original theorem by Fueter-Sce (assigning an R0,m-valued monogenic function to a C-valued holomorphic function) to the higher order case. We use this result to prove Fueter's theorem with an extra monogenic factor .     

On an extension of Rolle's theorem to locally convex spaces

This work concerns the extension of a weak form of the Rolle's theorem to locally convex spaces that satisfy an axiom of separation. The result provides a condition for asserting the uniqueness of a solution to nonlinear functional equations, including nonlinear integro-differential equations. We use the extended Rolle's theorem to prove the uniqueness of a solution to a nonlinear, fractional differential equation.