ITERATIVE APPROXIMATION OF FIXED POINTS FOR MULTIVALUED OPERATORS OF THE MONOTONE TYPE IN UNIFORMLY SMOOTH BANACH SPACES*

In this paper, let K be a nonempty subset of a uniformly smooth Banach space X, and T:K→2~k be a multivalued operator of the monotone type. The iterative sequence which converges strongly to the unique fixed point of T is given. Our results are the extension and improvements of the results obtained previously by several authors including Dunn, Chidume, Deng and Ding.     

Orlicz-Bochner函数空间中的单调点(英文)

本文主要研究了在赋予Orlicz范数与Luxemburg范数下Orlicz-Bochner函数空间中的一些单调点.     

ON THE UR AND WUR POINTS OF ORLICZ SEQUENCE SPACES

The criteria of UR and WUR points are given for the Orlicz sequence spaces.     

Orlicz序列空间的一致单调系数及应用

本文给出了Ｏｒｌｉｃｚ序列空间一致单调系数数值，同时给出了Ｏｒｌｉｃｚ序列空间具有一致单调性的条件，进而讨论具有一致单调性的Ｏｒｌｉｃｚ序列空间中的最佳逼近算子的一些特征。     

Upper (lower) monotone coefficient of a point in Orlicz function spaces

The calculation expressions of upper (lower) monotone coefficient of a point in Orlicz function spaces are given.     

赋Orlicz范数的Orlicz—Lorentz空间的严格凸性

本文对于赋Ｌｕｘｅｍｂｕｒｇ范数的Ｏｒｌｉｃｚ－Ｌｏｒｅｎｔｚ空间     

关于赋Luxemburg范数广义Orlicz序列空间的(J)非方点

本文研究了赋Luxemburg范数广义Orlicz序列空间的(J)非方点.通过分析、综合经典Orlicz空间与广义Orlicz空间的结构,给出了用生成函数表达该性质的充分必要条件.该结果不仅推广了经典空间的结果,也是十分好用的.     

Musielak-Orlicz序列空间的单调点

得到Ｍｕｓｉｅｌａｋ Ｏｒｌｉｃｚ序列空间中上（下）单调点和上（下）局部一致单调点的充分必要条件．     

赋范线性空间中同时远达点的唯一性

1 引言 设X为一实赋范线性空间,给定X中的子集G和有界子集K,令(?)和C分别表示X的所有非空有界子集与相对紧子集的全体,对A∈B,记 若x_(0)∈K满足sup||a-x_(0)||=Fk(A),则称x_(0)是A关于K的同时远达点,A关于K的同时远达点的全体记为Q_(K)(A),即     

Orlicz spaces without extreme points

Orlicz function and sequence spaces unit balls of which have no extreme points are completely characterized for both (the Orlicz and the Luxemburg) norms. Their subspaces of order continuous elements, with the norms induced from the whole Orlicz spaces without extreme points in their unit balls are also characterized. The well-known spaces L₁ and c₀ with unit balls without extreme points are covered by our results. Moreover, a new example of a Banach space without extreme points in its unit ball is given (see Example 1). This is the subspace a(L₁+L_∞) of order continuous elements of the space L₁+L_∞ equipped with the norm whenever 0<a<∞ and μ(T)>1/a.     

Banach空间中混合单调脉冲微分-积分方程解的存在性

本文给出了Banach空间中混合单调脉冲微分-积分方程解、耦合最小最大解的存在性定理及单调迭代方法,改进和推广了[1]-[4]的相应结果．     

空间中混合单调脉冲微分-积分方程解的存在性

利用两个新的比较结果，本文给出了Banach空间中混合单调脉冲微分-积分方程解，最小最大耦合解的存在性及单调迭代方法，改进和推广了[1-5]的相应结果．     

APPROXIMATION OF FIXED POINTS AND VARIATIONAL SOLUTIONS FOR PSEUDO-CONTRACTIVE MAPPINGS IN BANACH SPACES

Let K be a nonempty, closed and convex subset of a real reflexive Banach space E which has a uniformly Gteaux differentiable norm. Assume that every nonempty closed convex and bounded subset of K has the fixed point property for nonexpansive mappings. Strong convergence theorems for approximation of a fixed point of Lipschitz pseudo-contractive mappings which is also a unique solution to variational inequality problem involving φ-strongly pseudo-contractive mappings are proved. The results presented in this article can be applied to the study of fixed points of nonexpansive mappings, variational inequality problems, convex optimization problems, and split feasibility problems. Our result extends many recent important results.     

赋Orlicz范数的Musielak-Orlicz序列空间的单调点

给出赋Ｏｒｌｉｃｚ范数的Ｍｕｓｉｅｌａｋ－Ｏｒｌｉｃｚ序列空间中上（下）单调点以及上（下）局部一致单调点的充分必要条件．     

矢值Banach序列空间ss(E)的端点和强暴露点

本文讨论赋序列范数的矢值Banach序列空间ss(E)的几何性质．利用SS和SS(E)的关系刻化了ss(E)的端点和强暴露点，给出了它们的判据，并推广了lp(E)的结果．     

MIXED MONOTONE ITERATIVE TECHNIQUES FOR SEMILINEAR EVOLUTION EQUATIONS IN BANACH SPACES

This paper is concerned with initial value problems for semilinear evolution equations in Banach spaces. The abstract iterative schemes are constructed by combining the theory of semigroups of linear operators and the method of mixed monotone iterations. Some existence results on minimal and maximal (quasi)solutions are established for abstract semilinear evolution equations with mixed monotone or mixed quasimonotone nonlinear terms. To illustrate the main results, applications to ordinary differential equations and partial differential equations are also given.     

Musielak—Orlicz序列空间的光滑性质

本文给出了Ｍｕｓｉｅｌａｋ－Ｏｒｌｉｅｚ序列空间简洁的光滑点判据,从而得到十分便于应用的空间光滑性判别条件,同时纠正了「１」中主要定理的错误。     

Orlicz空间中具有函数型支撑的点

设０≠ｘ∈Ｌｍ,如果ｘ有（唯一）支撑泛函ｙ∈Ｓ（ＬＮ＾０）,．．．则称ｘ是具有（唯一）函数型支撑的点。本文在Ｏｒｌｉｃｚ空间ＬＭ（ＬＭ＾０,ｌＭ,ｌＭ＾０）中给出具有（唯一）函数型支撑的判定准则。     

赋序列范数的矢值Banach序列空间的强U-点和暴露点

刻划了赋序列范数的矢值Banach序列空间$ss(E)$的强U-点和暴露点,给出了它们的判据.     

一致光滑Banach空间中渐近伪压缩映象不动点的迭代逼近

本文研究用于逼近一致光滑Banach空间中渐近伪压缩映象不动点的具误差的修改了的Ishikawa 型与Mann型迭代程序的收敛性,改进和发展了文[1]的相应结果及他人的结果.