Banach空间中m-增生、奇算子的映射定理

利用连续线性泛函满足的某些条件,给出了关于ｍ－增生、奇算子的一些映射结果,这些结果是对已有文献中相应结果的改进．其中第二节中考虑了算子的奇性,运用Ｂｏｒｓｕｋ定理得出了ｍ一增生、奇算子的映射定理;在第三节中讨论了凝聚映射的相应结果．     

关于赋范线性空间中增生算子方程的逼近问题

研究了赋范线性空间中强增生映射和一致增生映射的零点的最速下降法迭代逼近问题,修正了Chidume的一个定理,改进和推广了Chidume和周海云等近期的相应结果.     

一类新的广义集值变分包含问题解的辅助序列迭代算法

本文提出并研究了Banach空间中的一类新的广义集值变分包含问题：0∈N（ω，y）＋A（z，v），由集值m-增生映射的预解算子建立了广义集值变分包含与不动点问题的等价性，并利用Nadler定理和辅助序列建立了一些迭代算法，证明了解的存在性和算法的全局收敛性．     

极大单调算子和m增生映射值域的扰动定理及在非线性微分方程上的应用

利用不动点定理,分别证明了在自反Banach空间中极大单调算子值域扰动的抽象结论和在H ilbert空间中m增生映射值域的扰动结果,这些结论是对以往一些工作的推广;然后,利用文中的新结论讨论了一类微分方程解的存在性.     

带紧扰动的M-增生算子的满值性定理

文中建立了算子A和C的若干满值性定理,其中A为m-增生算子而C为紧算子,所得结果推广并改进Zhu的主要结果.     

Banach空间中一类序压缩映射的不动点定理

在Banach空间中,利用迭代方法,研究了满足一定条件的序压缩算子的一些性质,获得了一类序压缩映射的不动点定理,证明了相应的结果,推广和改进了原有的结论,使其应用范围更加广泛.     

仿Fourier积分算子在非线性奇性传播中的应用

本文应用文献[1,2]中建立的仿Fourier积分算子概念以及仿微分算子的EropoB定理,对主型的仿微分算子进行微局部化简。并由此建立它们的奇性传播定理,然后用此定理讨论非线性方程解的低频奇性传播。     

有限级Fourier积分算子及其应用Ⅱ

本文继续讨论有限级Fourier 积分算子。在建立了这类算子的基本运算规则以后,我们证明了一般拟线性方程(包括非主型的方程)的解的奇性传播定理。并将这个结果应用于讨论一个非线性混合型方程与一个无旋定常流方程的解的奇性分析,得到了相应的奇性传播的结论。     

Hilbert空间内m-增生算子的扰动

<正> 本文提出了一个充分条件(定理1),足以保证复 Hilbert 空间 H 内一个线性 m-增生算子和一个增生算子的和为 m-增生的.这个条件似乎是同类型的条件中较弱的一种.复 Hilbert 空间 H 内一个线性算子 A(以 D(A)为其定义域 R(A)为其值域)叫做增生的,如果 R_e(A_μ,μ)≥0对所有μ∈D(A).如果更有 R(A+ξ)=H 对某一ξ>0成立(从而对所有ξ>0成立),我们就说 A 是 m-增生的.     

无穷个m增生映射公共零点和变分不等式解的杂交迭代算法及计算试验（英文）

本文设计一种新的杂交迭代算法用以逼近变分不等式的解集和两组无穷个m增生映射零点集的公共元.充分利用距离投影映射和豫解式算子的性质,证明一个强收敛定理.利用Visual Basic 6编程,通过计算机运算,验证迭代算法的有效性.本文把有限个算子的研究推广到无限个算子的情形并把抽象理论与计算机编程结合在一起,推广和补充了近期的相关研究工作.     

A new iterative algorithm for the variational inequality problem over the fixed point set of a firmly nonexpansive mapping

Many problems to appear in signal processing have been formulated as the variational inequality problem over the fixed point set of a nonexpansive mapping. In particular, convex optimization problems over the fixed point set are discussed, and operators which are considered to the problems satisfy the monotonicity. Hence, the uniqueness of the solution of the problem is not always guaranteed. In this article, we present the variational inequality problem for a monotone, hemicontinuous operator over the fixed point set of a firmly nonexpansive mapping. The main aim of the article is to solve the proposed problem by using an iterative algorithm. To this goal, we present a new iterative algorithm for the proposed problem and its convergence analysis. Numerical examples for the proposed algorithm for convex optimization problems over the fixed point set are provided in the final section.     

Extension operators via semigroups

The Roper-Suffridge extension operator and its modifications are powerful tools to construct biholomorphic mappings with special geometric properties. The first purpose of this paper is to analyze common properties of different extension operators and to define an extension operator for biholomorphic mappings on the open unit ball of an arbitrary complex Banach space. The second purpose is to study extension operators for starlike, spirallike and convex in one direction mappings. In particular, we show that the extension of each spirallike mapping is A-spirallike for a variety of linear operators A. Our approach is based on a connection of special classes of biholomorphic mappings defined on the open unit ball of a complex Banach space with semigroups acting on this ball.     

Most maximally monotone operators have a unique zero and a super-regular resolvent

Maximally monotone operators play important roles in optimization, variational analysis and differential equations. Finding zeros of maximally monotone operators has been a central topic. In a Hilbert space, we show that most resolvents are super-regular, that most maximally monotone operators have a unique zero and that the set of strongly monotone mapping is of the first category although each strongly monotone operator has a unique zero. The results are established by applying the Baire Category Theorem to the space of nonexpansive mappings.     

Set-valued mappings specified by regularization of the Schrödinger equation with degeneration

The Cauchy problem for the Schrödinger equation with an operator degenerating on a half-line and a family of regularized Cauchy problems with uniformly elliptic operators, whose solutions approximate the solution to the degenerate problem, are considered. A set-valued mapping is investigated that takes a bounded operator to a set of partial limits of values of its quadratic form on solutions of the regularized problems when the regularization parameter tends to zero. The dynamics of quantum states are determined by applying an averaging procedure to the set-valued mapping.     

Biholomorphic Mappings and the Extension Operators on New Hartogs Domains

In this paper, we generalize the Roper–Suffridge operator on the extended Hartogs domains.By using the geometric properties and the growth theorems of subclasses of biholomorphic mappings,we obtain the generalized operators preserve the properties of parabolic and spirallike mappings of type β and order ρ, S*_Ω(β, A, B), almost starlike mapping of complex order λ on ΩN under different conditions, and thus we get the corresponding results on the unit ball B~n in C~n. The conclusions lead to some known results.     

Equi-surjective systems of linear operators and applications

In this paper we study a system of linear operators between finite-dimensional Euclidean spaces. Emphasis is made on unbounded systems and sufficient conditions are established for their equi-surjectivity. An application is presented in which a system of approximate Jacobian matrices is used to obtain a parametric interior mapping theorem. A multiplier rule for vector problems is also derived.     

集值映射的连续选择与线性算子的齐性右逆

本文对于取值在Ｂａｎａｃｈ空间的几乎下半连续映射引入两个相关的下半连续闭凸集值映射,得到集值映射的连续选择存在性的若干特征,从而将 Ｄｅｕｔｓｃｈ Ｅ,和Ｋｅｎｄｅｒｏｖ Ｐ,Ｄｅ Ｂｌａｓｔ Ｆ．Ｓ．和 Ｍｙｊａｋ Ｊ,Ｐｒｚｅｓｌａｗｓｋｉ Ｋ．和 Ｒｙｂｉｎｓｋｉ Ｌ Ｅ,Ｇｕｔｅｖ Ｖ．等人以及作者自己的关于连续选择存在性的结果作为推论给出．并用这些结论讨论了在开映射定理不成立的。情况下从Ｂａｎａｃｈ空间到赋范空间上线性连续算子的齐性右逆存在问题．     

极大单调算子的扰动定理及在微分方程上的应用

利用不动点定理,首先证明了在自反Banach空间中极大单调算子扰动的抽象结论,这些结论是对以往一些工作的推广;然后,利用文中的新结论讨论了一类微分方程解的存在性.