共查询到20条相似文献,搜索用时 15 毫秒
1.
代宏霞 《应用泛函分析学报》2005,7(3):203-209
介绍了自反B anach空间中一类广义混合双线性型变分不等式,利用极大极小不等式和辅助变分原理技术证明了这类混合双线性型变分不等式解的存在性与唯一性. 相似文献
2.
Existence of Solutions and an Algorithm for Mixed Variational-Like Inequalities in Banach Spaces 总被引:3,自引:0,他引:3
X. P. Ding 《Journal of Optimization Theory and Applications》2005,127(2):285-302
In this paper, we study the class of mixed variational-like inequalities in reflexive Banach spaces. By applying a minimax
inequality due to the author, some existence and uniqueness theorems for solutions of mixed variational-like inequalities
are proved. Next, by applying the auxiliary problem technique, we suggest an innovative iterative algorithm to compute approximate
solutions of the mixed variational-like inequality. Finally, convergence criteria are also discussed.
This research was supported by NSF, Sichman Education Department of China, Projects 2003A081 and SZD0406.
The author expresses his sincere thanks to Professor H.P. Benson and the anonymous referees for careful comments leading to
the present version of this paper. 相似文献
3.
We consider a class of rearrangement invariant Banach Function Spaces recently appeared in a paper by the same authors, containing at the same time some Lorentz spaces Γ(ν), classical Lebesgue spaces and small Lebesgue spaces. We discuss the main properties coming directly from the norm, and, for certain values of the involved parameters, we prove some estimates of the norm of the associate space. 相似文献
4.
In this paper, by employing the notion of generalized projection operators and the well-known Fan’s lemma, we establish some
existence results for the variational inequality problem and the quasivariational inequality problem in reflexive, strictly
convex, and smooth Banach spaces. We propose also an iterative method for approximate solutions of the variational inequality
problem and we establish some convergence results for this iterative method.
L. C. Zeng, His research was partially supported by the Teaching and Research Award Fund for Outstanding Young Teachers in
Higher Education Institutions of MOE, China and by the Dawn Program Foundation, Shanghai, China.
J. C. Yao, His research was partially supported by the National Science Council of the Republic of China 相似文献
5.
介绍了集值映象的伪单调定义,并在Banach空间中构造了集值混和变分不等式问题近似解的迭代算法.应用伪单调映象定义,证明了该迭代算法收敛于集值混和变分不等式问题的近似解.特别值得注意的是:在文章中对集值映象没有Lipschitz连续性假设. 相似文献
6.
S.V. Astashkin F.A. Sukochev 《Journal of Mathematical Analysis and Applications》2007,336(2):1231-1258
We catalogue all Marcinkiewicz function and sequence spaces with the Banach-Saks property and present necessary and sufficient conditions for a wide subclass of spaces to possess the p-Banach-Saks property, 1<p<∞. We apply our results to several open problems. 相似文献
7.
This work is concerned with the analysis of convergence properties of feasible descent methods for solving monotone variational inequalities in Banach spaces. 相似文献
8.
Weighted Norm Inequalities for Marcinkiewicz Integrals with Non-Smooth Kernels on Spaces of Homogeneous Type 下载免费PDF全文
Hung Viet Le 《分析论及其应用》2022,38(2):204-231
In this article, we obtain some weighted estimates for Marcinkiewicz integrals with non-smooth kernels on spaces of homogeneous type. The weight $\omega$ considered here belongs to the Muckenhoupt’s class $A_∞.$ Moreover, weighted estimates for commutators of BMO functions and Marcinkiewicz integrals are also given. 相似文献
9.
在序Banach空间中,研究了一类集值混合单调映象,用不同方法证明了两个新的耦合不动点存在性定理,所做工作扩充了文[5]的研究成果. 相似文献
10.
用单调迭代的方法和一些新的比较结果,研究了Banach空间中一类事型非线性微分-积分方程的最大最小解,我们用空间E的弱完备性和锥P的正规性(这时可推出P是正则的)来代替紧性条件。 相似文献
11.
12.
To generalize the Hausdorff measure of noncompactness to other classes of bounded sets (like e. g. conditionally weakly compact or Asplund sets), we introduce Grothendieck classes. We deduce integral inequalities for quantities (called Grothendieck measures) related to these classes. As a by-product, we can answer a question concerning the measure of noncompactness for linear T : X → Y introduced in [14], and generalize a theorem about weak solutions of differential equations in Banach spaces. 相似文献
13.
Jesú s Bastero Francisco J. Ruiz 《Proceedings of the American Mathematical Society》1996,124(10):3183-3192
We give a very elementary proof of the reverse Hölder type inequality for the classes of weights which characterize the boundedness on of the Hardy operator for nonincreasing functions. The same technique is applied to Calderón operator involved in the theory of interpolation for general Lorentz spaces. This allows us to obtain further consequences for intermediate interpolation spaces.
14.
In this paper we pursue the study of the best approximation operator extended from L~Φ to L~φ, where φ denotes the derivative of the function Φ. We get pointwise convergence for the coefficients of the extended best approximation polynomials for a wide class of function f, closely related to the Calder′on–Zygmund class t_m~p(x) which had been introduced in 1961. We also obtain weak and strong type inequalities for a maximal operator related to the extended best polynomial approximation and a norm convergence result for the coefficients is derived. In most of these results, we have to consider Matuszewska–Orlicz indices for the function φ. 相似文献
15.
16.
Y. Chiang 《Journal of Global Optimization》2005,32(4):467-484
Let
(X, Z) be the space of continuous linear mappings between topological vector spaces, where Z is Hausdorff and preordered by
a closed convex cone C. In this paper, we introduce a notion of semicontinuity to any function from a topological space into
X. A notion of semicontinuity is also introduced to any function from a topological space into
(X, Z). These two notions of semicontinuity are related by the embedding of X into
(X, Z). Their basic properties are given. As an application, we derive some existence results for the mixed vector variational-like
inequality.
This work was partially supported by grants from the National Science Council of the Republic
of China. 相似文献
17.
18.
汪志明 《数学的实践与认识》2007,37(9):180-183
设E为一致光滑Banach空间,K为E的非空闭凸子集,T:K→K为Φ-强伪压缩映射.其中T=T1+T2,T1:K→K为Lipschitz映射,T2:K→K为具有有界值域映射.设{αn}n∞=0和{βn}n∞=0是[0,1]中满足一定条件的两实数列.则Ishikawa迭代序列{xn}∞n=0强收敛于T的唯一不动点. 相似文献
19.
In the paper we construct a system of bounded functions which generates an uncomplemented subspace in the Lorentz space Λ(α) for all α∈(0,1). Lower bounds of the norms of the projector onto such subspaces are obtained. Translated fromMatematicheskie Zametki, Vol. 68, No. 1, pp. 57–65, July, 2000. 相似文献
20.
在自反Banach空间中,研究了一类强增生型非线性变分包含解的存在性及其具有混合误差项的Ishikawa迭代程序的收敛性和稳定性问题,并提供了收敛率的估计.该文结果是一些作者早期与最近的相应结果的改进与推广. 相似文献