Banach空间中线性算子的齐性广义逆

本文首先在Banach空间内引进拟线性投影算子的概念,由此给出Banach空 间内线性算子的齐性广义逆的统一定义。齐性广义逆包含线性广义逆、单值度量广义 逆.本文证得齐性广义逆存在的充分必要条件.     

Banach空间中广义正交分解定理与广义正交可补子空间

本文首先将 Ｈｉｌｂｅｒｔ空间中的Ｒｉｅｓｚ正交分解定理推广到 Ｂａｎａｃｈ空间,得到 Ｂａｎａｃｈ空间广义正交分解定理．然后,利用此定理讨论由Ｊａｍｅｓ Ｒ．Ｃ．［１］引入的Ｂａｎａｃｈ空间中正交概念及 Ｎａｓｈｅｄ Ｍ．Ｚ．［２］引入的 Ｂａｎａｃｈ空间中（广义）正交可补子空间,得到判别子空间广义正交可补的充分必要条件,并由此给出Ｈｉｌｂｅｒｔ空间的一个新特征．     

广义正交分解定理与Tseng度量广义逆

本文将Banach空间中广义正交分解定理从线性子空间拓广至非线性集—太阳集,分别给出了一算子为度量投影算子和一度量投影算子为有界线性算子的充要条件;得到了判别Banach空间中子空间广义正交可补的充要条件;建立了王玉文和季大琴(2000年)新近引入的Banach空间中的线性算子的Tseng度量广义逆存在的特征刻划条件;这些工作本质地把王玉文等人的新近结果从自反空间拓广至非自反空间的情形.     

Newton-like methods in partially ordered Banach spaces

We provide convergence results and error estimates for Newton-like methods in generalized Banach spaces. The idea of a generalized norm is used whichis defined to be a map from a linear space into a partially ordered Banach space. Convergence results and error estimates are improved compared with the real norm theory.     

METRIC GENERALIZED INVERSE OF LINEAR OPERATOR IN BANACH SPACE＊＊＊

The Moore-Penrose metric generalized inverse T of linear operator T in Banach space is systematically investigated in this paper. Unlike the case in Hilbert space, even T is a linear operator in Banach Space, the Moore-Penrose metric generalized inverse T is usually homogeneous and nonlinear in general. By means of the methods of geometry of Banach Space, the necessary and sufficient conditions for existence, continuitv, linearity and minimum property of the Moore-Penrose metric generalized inverse T will be given, and some properties of T will be investigated in this paper.     

Banach 空间中一阶周期边值问题的广义解

In this paper, the authors study the periodic boundary value problems of a class of nonlinear integro-differential equations of mixed type in Banach space with Carath′eodory's conditions. We arrive at the conclusion of the existence of generalized solutions between general- ized upper and lower solutions, and develop the monotone iterative technique to find generalized extremal solutions as limits of monotone solution sequences in Banach space.     

Banach空间中线性算子的(集值)度量广义逆的表示及应用

在Banach空间Y无自反和从Banach空间X到Y的线性算子T无闭值域和稠定的假定下,利用Banach空间几何方法证明了Banach空间中线性算子的度量广义逆是具有闭凸值的集值映射,建立了该度量广义逆的存在性、唯一性和等价表达式,并给出了此表达式的一个应用示例．所得的部分结果本质地拓广王玉文和潘少荣在Banach空间Y自反,从X到Y的线性算子T为闭值域和稠定的假定下的近期相应结果．     

A Fixed Point Approach to the Fuzzy Stability of a Mixed Typ e Functional Equation

Through the paper, a general solution of a mixed type functional equation in fuzzy Banach space is obtained and by using the fixed point method a generalized Hyers-Ulam-Rassias stability of the mixed type functional equation in fuzzy Banach space is proved.     

A Moment Characterization of B-Valued Generalized Functionals of White Noise

Kernel theorems are established for Bananch space-valued multilinear mappings, A moment characterization theorem for Banach space-valued generalized functionals of white noise is proved by using the above kernel theorems. A necessary and sufficient condition in terms of moments is given for sequences of Banach space-valued generalized functionals of white noise to converge strongly. The integration is also discussed of functions valued in the space of Banach space-valued generalized functionals.     

一类含非紧映象方程的正解

本文定义了从一个Banach空间的相对开子集到另一个Banach空间的A-proper映象的广义相对拓扑度并且引入了广义P-紧和P₁-紧概念.其次,我们证明了含这些映象的方程的正解存在性定理.我们的定理改进和推广了最近的一些结果.     

A NEW PERTURBATION THEOREM FOR MOORE-PENROSE METRIC GENERALIZED INVERSE OF BOUNDED LINEAR OPERATORS IN BANACH SPACES

In this paper,we investigate a new perturbation theorem for the Moore-Penrose metric generalized inverses of a bounded linear operator in Banach space. The main tool in this paper is "the generalized Neumann lemma" which is quite different from the method in [12] where "the generalized Banach lemma" was used. By the method of the perturbation analysis of bounded linear operators,we obtain an explicit perturbation theorem and three inequalities about error estimates for the Moore-Penrose metric generalized inverse of bounded linear operator under the generalized Neumann lemma and the concept of stable perturbations in Banach spaces.     

Fixed Point Theorems and Convergence Theorems for a New Generalized Nonexpansive Mapping

Abstract

This paper introduces a new mapping that is weaker than nonexpansive mapping. The new mapping is different from the Suzuki’s generalized nonexpansive mapping. This paper introduces a new iteration process for the fixed point, and gives fixed point theorems and Convergence theorems for a new generalized nonexpansive mapping in Banach space, insteading of uniformly convex Banach space.     

Sturm-Liouville算子方程边值问题的最小极值解

利用 Banach空间中度量广义逆理论 ,证明了 LP(a,b)空间中 Sturm-Liouville算子方程边值问题最小极值解的存在性 ,并借助 Banach空间几何方法给出了最小极值解存在的等价条件     

Generalized Euler identity for subdifferentials of homogeneous functions and applications

In this paper, we mainly consider subdifferentials and basic subdifferentials of homogeneous functions defined on real Banach space and Asplund space respectively, and obtain the generalized Euler identity. As applications, we consider constrained optimization problems and several geometric properties of Banach space.     

Banach空间上的框架与拟Riesz基

该文首先给出Ｂａｎａｃｈ空间上的框架与拟Ｒｉｅｓｚ基的充要条件,其次讨论Ｂａｎａｃｈ空间上的框架和拟Ｒｉｅｓｚ基的稳定性,特别地,讨论在Ｂａｎａｃｈ空间上关于框架与拟Ｒｉｅｓｚ基的广义Ｐａｌｅｙ Ｗｉｅｎｅｒ定理．     

任意Banach空间中线性算子的Moore-Penrose度量广义逆

在无空间严格凸的几何假定下,利用Banach空间几何方法给出了任意Banach空间中线性算子T的Moore-Penrose度量广义逆T~+的存在性、唯一性、极小性和线性性的充要条件,同时还讨论了T~+的一些性质,这些本质地将文献[8]的最近结果从严格凸Banach空间拓广至任意Banach空间．     

Banach空间中线性算子的Tseng度量广义逆

在 Ｂａｎａｃｈ空间中,利用 Ｂａｎａｃｈ几何方法及度量投影算子,将 Ｅ．Ｈ．Ｍｏｏｒｓ的学生,曾远荣（Ｙ．Ｙ． Ｔｓｅｎｇ）在 Ｈｉｌｂｅｒｔ空间中为线性算子引入的 Ｔｓｅｎｇ广义道,推广到 Ｂａｎａｃｈ空间,引入 Ｔｓｅｎｇ度量广义逆（此时的 Ｔｓｅｎｇ度量广义逆一般为齐性算子,而非线性算子）,利用 Ｂａｎａｃｈ空间对偶映射与广义正交分解定理给出 Ｔｓｅｎｇ度量广义道存在的充分必要条件．讨论了最大Ｔｓｅｎｇ度量广义逆在最优化,控制论及微分方程不适定问题有着直接应用的一些基础性质．     

A first-order continuous method for the Antipin regularization of monotone variational inequalities in a Banach space

The concept of a generalized projection operator onto a convex closed subset of a Banach space is modified. This operator is used to construct a first-order continuous method for the Antipin regularization of monotone variational inequalities in a Banach space. Sufficient conditions for the convergence of the method are found.     

Strong convergence theorems by Halpern-Mann iterations for relatively nonexpansive mappings in Banach spaces

In this paper, we modify Halpern and Mann’s iterations for finding a fixed point of a relatively nonexpansive mapping in a Banach space. Consequently, a strong convergence theorem for a nonspreading mapping is deduced. Using a concept of duality theorems, we also obtain analogue results for certain generalized nonexpansive and generalized nonexpansive type mappings. Finally, we discuss two strong convergence theorems concerning two types of resolvents of a maximal monotone operator in a Banach space.