CFI算子和Weyl型定理(英文)

广义(ω)性质是Weyl定理的一种变形,它推广了由Rakocevic在[Matematicki Vesnik,1985,37(4):423-426]中引入的(ω)性质.本文利用一致Fredholm算子指标性质(CFT),给出了Hilbert空间上的有界线性算子满足广义(ω)性质的充要条件.另外还利用这一性质考虑了广义(ω_1)性质和(ω_1)性质的等价性.     

CFI算子和Weyl型定理(英文)北大核心CSCD

广义(ω)性质是Weyl定理的一种变形,它推广了由Rakocevic在[Matematicki Vesnik,1985,37(4):423-426]中引入的(ω)性质.本文利用一致Fredholm算子指标性质(CFT),给出了Hilbert空间上的有界线性算子满足广义(ω)性质的充要条件.另外还利用这一性质考虑了广义(ω_1)性质和(ω_1)性质的等价性.     

2×2上三角算子矩阵的广义(ω)性质(英文）

本文利用拓扑一致降标研究了Weyl定理的两个变形——广义(ω_1)性质及广义(ω)性质,给出了Hilbert空间中有界线性算子满足广义(ω_1)性质及广义(ω)性质的充要条件;最后,利用所得结果讨论了2×2上三角算子矩阵的广义(ω_1)性质及广义(ω)性质.     

一致Fredholm指标算子及广义(ω′)性质

本文给出了一致Fredholm指标算子的定义及判定,同时定义了Weyl型定理的一种新变化:广义(ω')性质.根据一致Fredholm指标性质定义出一种新的谱集,通过该谱集给出了Hilbert空间上有界线性算子满足广义(ω')性质的充要条件,并且研究了广义(ω')性质的摄动,还研究了算子的亚循环性和广义(ω')性质之间的关系.     

L-保序算子空间的ω-紧性

研究了L-保序算子空间的ω-紧性．借助于Hα-ω-开覆盖,定义了L-保序算子空间的ω-紧性,证明了ω-紧集和ω-闭集之交是ω-紧的,ω-紧性被连续的广义Zadeh型函数所保持,ω-紧性是L-好的推广,Tychonoff乘积定理成立．此外,给出了ω-紧性的网式刻画．     

一致可逆性质及广义(ω)性质的摄动

Hilbert空间算子T∈B(H)称为是一致可逆的,若对任意的S∈B(H),TS与ST的可逆性相同.本文中根据一致可逆性质定义了一个新的谱集,用该谱集来研究广义(ω)性质的稳定性,即考虑了Hilbert空间上有界线性算子的有限秩摄动、幂零摄动以及Riesz摄动的广义(ω)性质.之后研究了能分解成有限个正规算子乘积的一类算子的广义(ω)性质的稳定性.     

广义(ω′)性质的一个注记

(ω′)性质与广义(ω′)性质是Weyl定理的变形.研究了Hilbert空间上有界线性算子T及其T的演算有广义(ω′)性质的充要条件,然后利用所得的结论研究了控制类算子有广义(ω′)性质的充要条件.     

几类交换子在广义Morrey空间上的估计

设ωi(x,T)(i=1,2)是Rn×R+上的可测正函数,当(ω1,ω2)∈So,n时,由BMO函数与极大算子M生成的交换子,是从广义Morrey空间Lp,ω1(Rn)到Lp,ω2(Rn)的有界算子.对于奇异积分算子T以及Riesz积分位势算子Iα生成的交换子,也得到了相似的有界性结果.该结论推广了Mizuhara在广义Morrey空间上的相关结论.     

广义Kato分解与(ω)性质的稳定性判定

研究Hilbert空间上有界线性算子的(ω)性质,给出了广义Kato型的定义并根据广义Kato型的性质定义了一种新的谱集,利用该谱集给出了Hilbert空间上有界线性算子满足(ω)性质的充要条件,并且讨论了(ω)性质的稳定性.     

一类混合单调算子新的不动点定理及其应用

引入了广义Φ凹（-φ）凸算子这一概念,在非紧非连续条件下,得到了混合单调算子的几个新的不动点存在唯一性定理.最后给出了一个应用.     

On Concave Operators

We prove that a u0-concave operator can include other concave operators, and derive a sufficient and necessary condition for the existence and uniqueness of the fixed point of a kind of u0-concave operator under a weaker condition.     

A sum operator equation and applications to nonlinear elastic beam equations and Lane-Emden-Fowler equations

This paper is concerned with an operator equation Ax+Bx+Cx=x on ordered Banach spaces, where A is an increasing α-concave operator, B is an increasing sub-homogeneous operator and C is a homogeneous operator. The existence and uniqueness of its positive solutions is obtained by using the properties of cones and a fixed point theorem for increasing general β-concave operators. As applications, we utilize the fixed point theorems obtained in this paper to study the existence and uniqueness of positive solutions for two classes nonlinear problems which include fourth-order two-point boundary value problems for elastic beam equations and elliptic value problems for Lane-Emden-Fowler equations.     

一类非线性方程正解的存在唯一性

本文证明了形如Ａ＝Ｂ＋Ｃ的算子，其中Ｂ为线性算子，Ｃ为ψ－凹算子不动点的存在唯一及迭代收敛性，并将所获结果就用于常微分方程，偏微分方程和各人分方程得到了新的结论。     

Block Iterative Methods for a Finite Family of Generalized Nonexpansive Mappings in Banach Spaces

In this paper, we study an operator generated by a finite family of generalized nonexpansive mappings in a Banach space. We first prove that the set of fixed points of this operator is identical to the set of all common fixed points of the mappings. Next, using this operator, we construct an iterative sequence to approximate a common fixed point of the family of generalized nonexpansive mappings. We finally apply our results to solve the feasibility problem in Banach spaces.     

广义混合似变分不等式组的两步迭代算法

对H ilbert空间中一类广义混合似变分不等式组进行了研究;利用次微分算子的预解式技术,建立了广义混合似变分不等式组与不动点问题之间的等价关系;给出了一个求解这种广义混合似变分不等式组的显式两步迭代算法;并证明了该算法在适当的条件下收敛.     

Modified Ishikawa Iteration Process for Nonlinear Lipschitz Generalized Strongly Pseudo-Contractive Operators in Arbitrary Banach Spaces

In this paper, we modify the Ishikawa iteration process and show that such process, associated with a nonlinear Lipschitzian generalized strongly pseudo-contractive operator with a fixed point in a (not necessarily uniformly smooth) Banach space, converges strongly to the unique fixed point of this operator.     

一类(H,η)-单调算子的变分包含组

在Hilbert空间中,引入并研究一类新的关于(H,η)-单调算子的广义变分包含组问题.利用预解算子技巧和不动点定理证明了这类变分包含组解的存在性和唯一性.     

Continuity, compactness, and degree theory for operators in systems involving p-Laplacians and inclusions

The study of weak solutions for systems of nonlinear partial differential equations of elliptic type with inclusions leads to a multivalued operator of superposition type in Sobolev spaces. We show that, under natural assumptions, this operator has the properties which allow to apply degree theory (fixed point index) for multivalued maps. More precisely, this operator is upper semicontinuous and compact with nonempty convex compact values. For the particular case of systems involving p-Laplacians, we show that there is a homeomorphism transforming the whole system to a situation for which a fixed point index is available.     

有限个广义渐近非扩张映射具误差的复合隐迭代过程

在一致凸Banach空间研究了一个新的有限个广义渐近非扩张映射具误差的复合隐迭代过程.利用空间满足Opial条件和算子满足半紧性条件,我们证明了这个隐迭代过程强、弱收敛于有限个广义渐近非扩张映射的公共不动点.这些结果是目前所得成果的完善和推广.     

On generalized operator quasi-equilibrium problems

In this paper, we will introduce the generalized operator equilibrium problem and generalized operator quasi-equilibrium problem which generalize the operator equilibrium problem due to Kazmi and Raouf [K.R. Kazmi, A. Raouf, A class of operator equilibrium problems, J. Math. Anal. Appl. 308 (2005) 554-564] into multi-valued and quasi-equilibrium problems. Using a Fan-Browder type fixed point theorem in [S. Park, Foundations of the KKM theory via coincidences of composites of upper semicontinuous maps, J. Korean Math. Soc. 31 (1994) 493-519] and an existence theorem of equilibrium for 1-person game in [X.-P. Ding, W.K. Kim, K.-K. Tan, Equilibria of non-compact generalized games with L^∗-majorized preferences, J. Math. Anal. Appl. 164 (1992) 508-517] as basic tools, we prove new existence theorems on generalized operator equilibrium problem and generalized operator quasi-equilibrium problem which includes operator equilibrium problems.