Adjoint Linear Systems on Normal Log Surfaces

We prove a Reider type theorem for separating any cluster by an adjoint system to a pseudoeffective divisor on a normal surface. As a corollary we get a Reider type theorem for adjoint linear systems (to a nef Q-divisor) on normal log surfaces. This theorem is new even for smooth surfaces.     

一个新的Ky Fan匹配定理及其在L-凸度量空间中的应用

建立了转移开覆盖的一个新的Ky Fan型匹配定理．作为应用，获得了Fan-Browder重合定理，不动点定理、极大元定理，相交定理和截口定理．     

A Radon–Nikodym type theorem for forms

The Lebesgue decomposition theorem and the Radon–Nikodym theorem are the cornerstones of the classical measure theory. These theorems were generalized in several settings and several ways. Hassi, Sebestyén, and de Snoo recently proved a Lebesgue type decomposition theorem for nonnegative sesquilinear forms defined on complex linear spaces. The main purpose of this paper is to formulate and prove also a Radon–Nikodym type result in this setting. As an application, we present a Lebesgue type decomposition theorem and solve a special case of the infimum problem for densely defined (not necessarily bounded) positive operators.     

Generalized KKM type theorems in FC-spaces with applications (II)

This paper is a continuum of the preceding paper of author. By applying a coincidence theorem in noncompact FC-space without any convexity structure due to author, a new KKM type theorem is first proved under noncompact setting of FC-spaces. The equivalent relation between the coincidence theorem and the KKM type theorem is also established. As applications of the KKM type theorem, we establish some new existence theorems of solutions for three classes of generalized vector equilibrium problems under noncompact setting of FC-spaces. These theorems improve and generalize many known results in literature.     

Generalized quasiconvexities,cone saddle points,and minimax theorem for vector-valued functions

We establish the following theorems: (i) an existence theorem for weak type generalized saddle points; (ii) an existence theorem for strong type generalized saddle points; (iii) a generalized minimax theorem for a vector-valued function. These theorems are generalizations and extensions of the author's recent results. For such extensions, we propose new concepts of convexity and continuity of vector-valued functions, which are weaker than ordinary ones. Some of the proofs are based on a few key observations and also on the Browder coincidence theorem or the Tychonoff fixed-point theorem. Also, the minimax theorem follows from the existence theorem for weak type generalized saddle points. The main spaces with mathematical structures considered are real locally convex spaces and real ordered topological vector spaces.This paper is dedicated to Professor Kensuke Tanaka on his sixtieth birthday.This paper was written when the author was a visitor at the Department of Mathematical Science, Graduate School of Science and Technology, Niigata University, Niigata, Japan. The author is indebted to Prof. K. Tanaka for suggesting this work.The author is very grateful to Prof. P. L. Yu for his useful encouragement and suggestions and to the referees for their valuable suggestions and comments.     

紧开覆盖的一个新的Ky Fan型匹配定理及其应用

建立了紧开覆盖的一个新的Ky Fan型匹配定理.作为应用,研究了Fan-Browder型重合定理、Ky Fan型最佳逼近定理、极大元定理及超凸空间中的定性对策和抽象经济的平衡存在定理.     

L-空间中的KKM映射及不动点定理

引入了L-空间和L-空间上的KKM类映射，建立了关于该类映射的一些不动点定理，其中包括Schauder型和Fan-Browder型不动点定理．得到了L-空间中的KyFan匹配定理和叠合点定理．     

齐次群上二阶半线性偏微分方程的一类Picone型恒等式和Sturmian比较定理

本文给出了齐次群上的一类广义Picone型恒等式,由此证明了以下半线性方程组(其中 表示齐次群上的广义梯度)的Sturmian比较定理及一类振荡定理,并用于Heisenberg群上一类半线性方程.然后利用这里的广义Picone型恒等式证明了Heisenberg群上一类更一般的Hardv型不等式     

Remarks on acyclic versions of generalized von Neumann and Nash equilibrium theorems

A fixed-point theorem on compact compositions of acyclic maps on admissible (in the sense of Klee) convex subset of a t.v.s. is applied to obtain a cyclic coincidence theorem for acyclic maps, generalized von Neumann type intersection theorems, the Nash type equilibrium theorems, and the von Neumann minimax theorem. Our new results generalize earlier works of Lassonde [1], Simons [2], and Park [3,4].     

A refinement of Sharkovskii's theorem on orbit types characterized by two parameters

The so-called type problem or forcing problem is considered as a way to generalize Sharkovskii's theorem. In this paper, by focusing on certain types of orbits, we obtain a solution of the type problem, which gives a refinement of Sharkovskii's theorem on orbit types characterized by two parameters.     

一般化凸空间上的Ky Fan型重合点定理及其应用

我们应用已有的一般化凸空间上的KKM型定理得到K y Fan型重合点定理,然后作为应用给出截口定理和择一性问题.我们的主要结果对文[1-5]中的相应的结果进行了改进和一般化.     

ON LIMITING PROPERTIES OF BERNSTEIN-TROTTER TYPE OPERATOR

In this paper ,a class of Bernstein-Trotter type operator and its limiting properties are studied. By using both the limiting theorem and P. Le‘ vy continuity theorem on probability theory, a theorem of convergence is obtained. The result in [1] is included.     

Fixed points of approximable maps

We present a simple proof of the Leray-Schauder type theorem for approximable multimaps given recently by Ben-El-Mechaiekh and Idzik. We apply this theorem to obtain a Schaefer type theorem, the Birkhoff-Kellogg type theorems, a Penot type theorem for non-self-maps, and quasi-variational inequalities, all related to compact closed approximable maps.

     

Infinite dimensional Cauchy-Kowalevski and Holmgren type theorems

The aim of this paper is to show Cauchy-Kowalevski and Holmgren type theorems with an infinite number of variables. We adopt von Koch and Hilbert's definition of analyticity of functions as monomial expansions. Our Cauchy-Kowalevski type theorem is derived by modifying the classical method of majorants.Based on this result, by employing some tools from abstract Wiener spaces, we establish our Holmgren type theorem.     

从O.Stolz定理到L’Hospital法则

阐述了应用Stolz定理求数列极限时应注意的问题,并从Stolz定理与L’Hospital法则相互呼应的角度,指出了∞∞型的L’Hospital法则可改进为*∞型.这些工作,不但扩大了其应用范围,而且还给求极限带来许多方便.     

一般化凸空间上极大极小不等式及其应用

我们首先改进了已有的KKM型定理,然后根据改进后的KKM型定理得到了一般化凸空间上的KyFan型极大极小不等式,最后利用它给出了Fan-Kneser型不等式族及其一些应用.我们的结论对文献中的相应结果进行了改进和一般化。     

Pseudolocality of the Ricci Flow Under Integral Bound of Curvature

We prove a pseudolocality type theorem for compact Ricci flows under local integral bounds on curvature. The main tool we use here is the local Ricci flow introduced by Deane Yang and the pseudolocality theorem due to Perelman. We also prove a theorem on the extension of the local Ricci flow.     

Paley–Wiener–Schwartz type theorem for the wavelet transform

In the present paper, we discuss about extension of the wavelet transform on distribution space of compact support and develop the Paley–Wiener–Schwartz type theorem for the wavelet transform on the same. Furthermore, Paley–Wiener–Schwartz type theorem for the wavelet transform is also established using the relation between the wavelet transform and double Fourier transform.     

Scalar derivatives and scalar asymptotic derivatives. An Altman type fixed point theorem on convex cones and some applications

An Altman type fixed point theorem, on a convex cone in a Banach space, will be presented. In this theorem we replace the classical Altman's condition by an asymptotic condition. Also, we will establish some relations between this Altman type fixed point theorem and the scalar derivatives. Some applications will be given.     

The first eigenvalue of Finsler p-Laplacian

The eigenvalues and eigenfunctions of p-Laplacian on Finsler manifolds are defined to be critical values and critical points of its canonical energy functional. Based on it, we generalize some eigenvalue comparison theorems of p-Laplacian on Riemannian manifolds, such as Lichnerowicz type estimate, Obata type theorem and Mckean type theorem, to the Finsler setting. Not only that, the Lichnerowicz type estimate we obtained is even better than the corresponding one in Riemannian geometry.